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Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Accountancy Guide Pdf Chapter 8 Financial Statement Analysis Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Accountancy Solutions Chapter 8 Financial Statement Analysis

12th Accountancy Guide Financial Statement Analysis Text Book Back Questions and Answers

I Multiple Choice Questions

Choose the correct answer

Question 1.
Which of the following statements is not true?
(a) Notes and schedules also form part of financial statements.
(b) The tools of financial statement analysis include common -size statement
(c) Trend analysis refers to the study of movement of figures for one years
(d) The common-size statements show the relationship of various items with some common base, expressed as percentage of the common base.
Answer:
(c) Trend analysis refers to the study of movement of figures for one years

Question 2.
Balance sheet provides information about the financial position of a business concern
(a) Over a period of time
(b) As on a particular date
(c) For a period of time
(d) For the accounting period
Answer:
(b) As on a particular date

Question 3.
Which of the following tools of financial statement analysis is suitable when data relating to several years are to be analysed?
(a) Cash flow statement
(b) Common size statement
(c) Comparative statement
Answer:
(d) Trend analysis

Question 4.
The financial statements do not exhibit
(a) Non-monetary data
(b) Past data
(c) Comparative statement
(d) Standard costing
Answer:
(a) Non-monetary data

Question 5.
Which of the following is not a tool of financial statement analysis?
(a) Trend analysis
(b) Common size statement
(c) Comparative statement
Answer:
(d) Standard costing

Question 6.
The term fund’ refers to
(a) Current liabilities
(b) Working capital
(c) Fixed assets
(d) Non-current assets.
Answer:
(b) Working capital

Question 7.
Which of the following statement is not true?
(a) All the limitations of financial statements are applicable to financial statement analysis also.
(b) Financial statement analysis is only the means and not an end.
(c) Expert knowledge is not required in analyzing the financial statements
(d) Interpretation of the analysed data involves personal judgment.
Answer:
(c) Expert knowledge is not required in analyzing the financial statements

Question 8.
A limited company’s sales have increased from ‘ 1,25,000 to 1,50,000. How does this appear in the comparative income statement?
(a) +20%
(b) +120%
(c) -120%
(d) -20%
Hint:
Percentage increase or Decrease = \(\frac{\text { Absolute amount of increase or decrease }}{\text { Year } 1 \text { amount }}\) × 100
Sales increase = ₹ 1,25,000 – ₹ 1,50,000 = ₹ 25,000
\(\frac{25,000}{1,25,000}\) × 100 = +20% = 1,25,000
Answer:
(a) +20%

Question 9.
In a common-size balance sheet, if the percentage of non-current assets is 75, what would be the percentage of current assets?
(a) 175
(b) 125
(c) 25
(d) 100
Hint:
Let Assets = ₹ 100
Non current assets = ₹ 75
∴ Current assets = 100 – 75 = 25
Answer:
(c) 25

Question 10.
Expenses for a business for the first year were ₹ 80,000. In the second year, it was increased to ₹ 88,000. What is the trend percentage in the second year?
(a) 10%
(b) 110%
(c) 90%
(d) 11%
Hint:
Computation of trend percentage = \(\frac{\text { Other year }}{\text { Earliest base year }}\) × 100
Earliest base year x 100
For second year = \(\frac{88,000}{80,000}\) × 100 = 110%
Answer:
(b) 110%

II Very Short Answer Questions

Question 1.
What are the financial statements?
Answer:
Financial statements are the statements prepared by the business concerns at the end of the accounting period to ascertain the operating results and the financial position.

Question 2.
List the tools of financial statement analysis.
Answer:

• Comparative statement
• Common size statements
• Trend analysis
• Funds flow statement
• Cash flow analysis

Question 3.
What is working capital?
Answer:
The term ’fund’ refers to working capital. Working capital refers to the excess of current assets over current liabilities.

Question 4.
When is trend analysis preferred to other tools?
Answer:
Trend analysis discloses the changes in financial and operating data between specific periods when data for more than two years are to be analyzed. It may be difficult to use a comparative statement.

III Short Answer Questions

Question 1.
‘Financial statements are prepared based on past data’. Explain how this is a limitation.
Answer:
The nature of the financial statement is historical. Past cannot be the index of the future and cannot be cent percent basis for future estimation, forecasting, budgeting, and planning.

Question 2.
Write a short note on cash flow analysis?
Answer:
Cash flow analysis is concerned with the preparation of a cash flow statement which shows * the inflow and outflow of cash and cash equivalents in a given period of time. Cash includes cash in hand and demand deposits with banks. Cash equivalents denote short term investments which can be realized easily within a short period of time, without much loss in value. Cash flow analysis helps in assessing the liquidity and solvency of a business concern.

Question 3.
Briefly explain any three limitations of financial statements.
Answer:

1. Lack of qualitative information: Qualitative information, that is non – monetary information is also important for business decisions. For example Efficiency of the employees and efficiency of the management. But this is ignored in financial statements.
2. Record of historical data: Financial statement are prepared based on historical data. They may not reflect the current position.
3. Ignores price level changes: Adjustments for price level changes are not made in the financial statements. Hence financial statements may not reveal the current position.

Question 4.
Explain the steps involved in preparing comparative statements?
Answer:
Following are the steps to be followed in preparation of the comparative statement:

1. Column 1: In this column, particulars of items of income statement or balance sheet are written.
2. Column 2: Enter absolute amount of year 1.
3. Column 3: Enter absolute amount of year 2.
4. Column 4: Show the difference in amounts between year 1 and year 2. If there is an increase in year 2, put plus sign and if there is decrease put minus sign.
5. Column 5: Show percentage increase or decrease of the difference amount shown in column 4 by dividing the amount shown in column 4 (absolute amount of increase or decrease) by column 2 (year 1 amount).

That is,
Percentage increase or decrease = \(\frac{\text { Absolute amount of increase or decrease }}{\text { Year } 1 \text { amount }}\) × 100

Question 5.
Explain the procedure for preparing a common – Size statement.
Answer:
Common-size statements can be prepared with three columns. Following are the steps to be followed in the preparation of the common – size statement.

1. Column 1. In this column, the particulars of items of the income statement or balance sheet are written.
2. Column 2. Enter the absolute amount.
3. Column 3. Choose a common base as 100.

For example Revenue from operations can be taken as the base for income statement and total of the balance sheet can be taken as the base for the balance sheet. Work out the percentage for all the items of column 2 in terms of the common base and enter them in column 3.

IV Exercises

Comparative statement analysis

Question 1.
From the following particulars, prepare a comparative income statement of Arul Ltd.

Solution:
The comparative income statement of Arul Ltd for the year ended 31.3.16 & 31.3.17

Answer :
Revenue from operation: 20 %;
Other income: 200%;
Total revenue: 50%;
Expenses: 25%;
Profit before tax: 100%

Question 2.
From the following particulars, prepare a comparative income statement of Barani Ltd.

Solution:
Computation of % increase for revenue from operation
Percentage increase = \(\frac{15,000}{30,000}\) × 100 = 50%
Comparative Income statement of Barani Ltd. for the year ended 31.3.17 & 31.3.18


Answer :
Revenue from operations: 50%
Other income: 50%
Total revenue: 50%
Expenses: 50%;
Profit before tax: 50%;
Profit after tax: 50%

Question 3.
From the following Particulars, prepare comparative income ‘statement of Daniel Ltd.

Solution:
The comparative Income statement of Daniel Ltd. for the year ended 31.3.16 & 31.3.17

Answer :
Revenue from operations: 25%
Expenses: 10%
Tax: 50%;
Profit before tax: 50%;
Profit after tax: 50%

Question 4.
From the following particulars, prepare a comparative .statement of the financial position of Muthu Ltd.

Solution:
Comparative B/s of Muthu Ltd. As on 31.3.17 & 31.3.18

Answer :
Shareholder’s fund: 10%;
Non-current liabilities: 10%
current liabilities: 10%
Total equity and liabilities: 10%;
Non -current assets: 20%;
Current assets: 30%
Total Assets: 10%

Question 5.
From the following particulars, prepare a comparative statement of the financial position of Kala Ltd.


Solution:



Answer :
Share capital: 20%;
Reserves and surplus: Nil.
Non-Current liabilities: -20%;
Current liabilities: -40%;
Total equity and liabilities: 10%;
Fixed assets: 16%;
Non-current investments: -20%;
Inventories: 25%;
Cash and cash equivalents: 20%;
total assets: 10%

Question 6.
Prepare a common-size income statement for the following particulars Raja Ltd. for the year ended 31st March 2017.

Solution:

Answer :
2016-2017:
Other income: 15%
total revenue: 115%
Expenses: 30%
Profit before tax: 85%

Question 7.
From the following particulars of Maria ltd and Kala Ltd. Prepare a common-Size income statement for the year ended 31st March 2019.

Solution:


Answer :
Maria Ltd: Other Income: 10%; total revenue: 110%; Expenses: 70%; Profit before tax:40%
Kala Ltd: Other income: 15%; Total revenue: 115% Expenses: 60%; Profit before tax:55%

Question 8.
Prepare a common-size income statement for the following particulars of Sam Ltd. table

Solution:

Answer :
2015-16: Other income:20%; Total revenue: 120% Expenses:60%; Profit before tax:60%: Tax: 18%; Profit after tax:42%;
2016-17: Other income: 10%; total revenue: 110%; Expenses:50%; Profit before tax: 60%: Tax:18%;
Profit after tax:42%

Question 9.
Prepare Common-size balance sheet of Meena Ltd. as of 31st March 2018.

Solution:
Common size B/s Meena Ltd as on 31.3.18


Answer :
Shareholder’s fund:50%; Non-current liabilities: 40%; Current liabilities: 10%; Non-current assets:75%; current assets:25%

Question 10.
Prepare a common-size statement of financial position for the following particulars of Rani Ltd.

Solution:


Answer :
2015-16 Shareholder’s fund:60%; Non-current liabilities: 30%; Current liabilities: 10%; Non-current assets:80%; current assets:20%
2016-17 Shareholder’s fund:60%;Non-current liabilities: 25%; Current liabilities: 15%; Non-current assets:80%; Current assets:20%

Question 11.
Prepare a common-size statement of financial position for the following particulars of Yasmin Ltd. and Sakthi Ltd.


Solution:


Answer:
Yasmin Ltd: Share capital 40%; Reserves and surplus: 10%; Noncurrent liabilities:30%; current liabilities:20%. Fixed assets:40%; Non -Current investments: 10% Inventories:40%; Cash & cash equivalents: 10% Sakthi Ltd: Share „ capital: 50%; Reserves and surplus: 10%; Non-current liabilities:30%; Current liabilities: 10%; Fixed assets:50% Non-current investmesits:20%; Inventories: 15% cash & cash equivalents: 15%
Trend Analysis:

Question 12.
From the following particulars, calculate the trend percentages of Kala Ltd.

Solution:

Answer:
2016-17: Revenue from operations: 125%; Other income: 150%; Total revenue: 130% Expenses:145% Profit before tax: 120%
2017-18: Revenue from operations: 150%; Other income 200%; Total revenue: 160% Expenses:175%; Profit before tax: 150%

Question13.
From the following particulars, calculate the Trend percentages of Kavitha Ltd.

Solution:

Answer:
2016-17: Revenue from operations: 125%; Other income: 125%; total revenue:125%; Expenses: 120%; Profit before tax:150%; Tax :150%; Profit after tax: 150%;
2017-2018; Revenue from operations: 150%; Other income:150%; total revenue:150% Expenses:80%; Profit before tax: 500% Tax:500%; Profit after tax:500%

Question 14.
From the following particulars, calculate the trend percentage of Kumar Ltd.

Solution:

Answer :
2016-17: Revenue from operations:90%; Other income: 160%; total revenue: 100%; Expenses:80%; Profit before tax: 150%; Tax: 150%; Profit after tax:150%;
2017-18: Revenue from operations:50%; Other income: 120%; total revenue:60%; Expenses:50%; Profit before tax: 85%; Tax:85%; Profit after tax:85%

Question 15.
From the following particulars, calculate the trend percentages of Anu Ltd.

Solution:


Answer :
year 2: Shareholder’s Fund: 110%, Non-current liabilities: 125%; Current liabilities:80%; Total equity and liabilities: 110%; Non-Current assets: 120%, Current assets:80%; total assets: 10%;
year 3: Shareholder’s fund: 120%; Non- current liabilities: 120%; Current liabilities: 120% Total equity and liabilities: 120%; Non-current assets: 130% Current assets:90%; total assets: 120%

Question 16.
From the following particulars, calculate the trend percentages of Babu Ltd.

Solution:



Answer:
Year 2: Share capital: 127%; Reserves and surplus: 100%; Non-current liabilities: 110%; Current liabilities: 150% Total equity and liabilities: 120%; Fixed assets:118%; Non-current investments: 125%; Inventories:! 10%; Cash & cash equivalents: 150%; total assets:120%;
Year 3: Share capital: 106%; Reserves and surplus :150%; Non-current liabilities: 120%; Current liabilities: 200%; total equity and liabilities: 125%; Fixed assets:103%; Non – Current investments: 150%; Inventories: 120%; Cash & cash equivalents:200%; total assets: 125%

12th Accountancy Guide Financial Statement Analysis Additional Important Questions and Answers

Other Important questions & Answers

Question 1.
…………………………. are the tools of financial analaysis
(a) Comparative statements
(b) Trend analysis
(c) Common size statement
(d) all the above
Answer:
(d) all the above

Question 2.
Analysis of financial statements involves
(a) B/S
(b) Trading A/c
(c) All the above
Answer:

III Short Answer Questions

Question 1.
What are the features of a financial statement?
Answer:
Following are the features of financial statements:

• Financial statements are generally prepared at the end of an accounting period based on transactions recorded in the books of accounts.
• These statements are prepared for the organization as a whole.
• Information is presented in a meaningful way by grouping items of similar nature such as fixed assets.
• Financial statements are prepared based on historical cost.
• Financial statements are prepared based on accounting principle and Accounting Standards, which make financial statements comparable and realistic.
• Financial statements involve personal judgment in a certain case. For example, the selection of the method of depreciation, percentage of reserve, etc.

Question 2.
Explain the significance of financial statements.
Answer:
Financial statements reveal the operating results and financial position of the business concern. The significance of financial statements to various stakeholders is as follows:

• To Management: Financial statements provide information to the management to take decision and to have control over business activities, in various areas.
• To shareholders: Financial statements help the shareholders to know whether the business has potential for growth and to decide to continue their shareholding.
• To potential investors: Financial statements help to value the securities and compare it with those of other business concerns before making their investment decisions.
• To creditors: Creditors can get information about the ability of the business to repay the debts from financial statements.
• To bankers: Information given in the financial statements is significant to the bankers to assess whether there is adequate security to cover the amount of the loan or overdraft.
• To the government: Financial statements involve personal judgment in a certain case. For example, the selection of the method of depreciation, percentage of reserve, etc.
• To employees: Through the financial statements, the employees can assess the ability of the business to pay salaries and whether they have future growth in the concern.

Question 3.
Explain the provisions of the Indian Companies Act 2013 to be followed while preparing the financial statement of or company.
Answer:
Following provisions of the Indian Companies Act, 2013 have to be followed while preparing the financial statements of a company:

• As per Section 2(40), financial statements include balance sheet, profit and loss account/income and expenditure account, cash flow statement, statement of changes in equity and any explanatory note annexed to the above.
• Section 129 (1) of the Indian Companies Act, 2013 states that the financial statements shall give a true and fair view of the state of affairs of the company and shall comply with the Accounting Standards notified under section 133.
• Section 129 (1) also states that the financial statements shall be prepared in the form provided in schedule III of the Indian Companies Act, 2013.

Question 4.
What do you mean by financial statement analysis?
Answer:
Financial statement analysis is a comparison of the various items in the financial statement by establishing and evaluating relationships among them so that, it gives a better understanding of the performance and financial status of the business concern.

Question 5.
What are the objectives of financial statement analysis?
Answer:
Financial statement analysis may be done with any of the following objectives:

• To analyze profitability and earning capacity.
• To study the long term and short term solvency of the business.
• To determine the efficiency in operations and use of assets.
• To determine the efficiency of management and employees.
• To determine the trend in sales, production, etc.
• To forecast for the future and prepare budgets.
• To make inter-firm and intra-firm comparisons.

Question 6.
What are the limitations of fin. State analysis.
Answer:
Following are the limitations of financial statement analysis:
1. All the limitations of financial statements such as ignoring non-monetary information, ignoring price level changes, etc., are applicable to financial statement analysis also.

2. Financial statement analysis is only the means and not an end, that is, it is only a tool in the hands of management and other shareholders. Interpretation of the results has to be done only by the financial analysts with due regard to the internal and external environmental factors.

3. Expert knowledge is required in analyzing the financial statements.
4. Interpretation of the analyzed data involves personal judgments as different experts may give different views.

Question 7.
What do you mean by Horizontal analysis?
Answer:
Horizontal analysis
When figures relating to several years are considered for the purpose of analysis, the analysis is called horizontal analysis. Generally, one year is taken as the base year and the figures relating to the other years are compared with that of the base year. Comparative statements and trend percentages are examples of horizontal analysis.

Question 8.
What do you mean by vertical analysis?
Answer:
Vertical analysis
When figures relating to one accounting year alone are considered for the purpose of analysis, the analysis is called vertical analysis. Here, the relationship is established among items from various financial statements relating to the same accounting period. Preparation of common size statements and computation of ratios are examples of vertical analysis.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 9 Applications of Integration Ex 9.10 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.10

Choose the most suitable answer from the given four alternatives:

Question 1.
The value of \(\int_{0}^{2/3}\) \(\frac { dx }{ \sqrt{4-9x^2} }\)
(a) \(\frac { π }{ 6 }\)
(b) \(\frac { π }{ 2 }\)
(c) \(\frac { π }{ 4 }\)
(d) π
Solution:
(a) \(\frac { π }{ 6 }\)
Hint:

Question 2.
The value of \(\int_{-1}^{2}\) |x| dx
(a) \(\frac { 1 }{ 2 }\)
(b) \(\frac { 3 }{ 2 }\)
(c) \(\frac { 5 }{ 2 }\)
(d) \(\frac { 7 }{ 2 }\)
Solution:
(c) \(\frac { 5 }{ 2 }\)
Hint:
|x| = x if x > 0
= -x if x < 0

Question 3.
For any value of n ∈ Z \(\int_{0}^{π}\) e^cos²x cos3 [(2n + 1) x] dx
(a) \(\frac { π }{ 2 }\)
(b) π
(c) 0
(d) 2
Solution:
(c) 0
Hint:

Question 4.
The value of \(\int_{-π/2}^{π/2}\) sin² x cos x dx
(a) \(\frac { 3 }{ 2 }\)
(b) \(\frac { 1 }{ 2 }\)
(c) 0
(d) \(\frac { 2 }{ 3 }\)
Solution:
(d) \(\frac { 2 }{ 3 }\)
Hint:
f(x) = sin²x cos x
f(-x) = sin²(-x) cos(-x) = sin²x cos x
f(x) = f(-x)
f is an even function

Question 5.
The value of \(\int_{-4}^{4}\)[tan^-1(\(\frac { x^2 }{ x^4+1 }\)) + tan^-1(\(\frac { x^4+1 }{ x^2 }\))] dx
(a) π
(b) 2π
(c) 3π
(d) 4π
Solution:
(d) 4π
Hint:

Question 6.
The value of \(\int_{-π/4}^{π/4}\) (\(\frac { 2x^7-3x^5+7x^3-x+1 }{ cos^2x }\)) dx is
(a) 4
(b) 3
(c) 2
(d) 0
Solution:
(c) 2
Hint:

Odd function – 3 Odd function + 7 Odd function – Odd function + even function
= 0 + 2 \(\int_{0}^{π/4}\) sec² x dx
= 2 [tan x]\(_{0}^{π/4}\)
= 2(1 – 0)
= 2

Question 7.
If f(x) = \(\int_{0}^{x}\) cos t dt, then \(\frac { df }{ dx }\) =
(a) cos x – x sin x
(b) sin x + x cos x
(c) x cos x
(d) x sin x
Solution:
(c) x cos x
Hint:
f(x) = \(\int_{0}^{x}\) cos t dt
u = t, dv = cos t dt
u’ = 1, v = sin t
v₁ = -cos t
f(x) = [t sin t + cos t]\(_{0}^{x}\)
f(x) = x sin x + cos x – 1
\(\frac { df }{ dx }\) = x cos + sin x – sin x
\(\frac { df }{ dx }\) = x cos x

Question 8.
The area between y² = 4x and its latus rectum is
(a) \(\frac { 2 }{ 3 }\)
(b) \(\frac { 4 }{ 3 }\)
(c) \(\frac { 8 }{ 3 }\)
(d) \(\frac { 5 }{ 3 }\)
Solution:
(c) \(\frac { 8 }{ 3 }\)
Hint:
y² = 4x
y = 2√x

Question 9.
The value of \(\int_{0}^{1}\) x (1 – x)⁹⁹ dx is
(a) \(\frac { 1 }{ 11000 }\)
(b) \(\frac { 1 }{ 10100}\)
(c) \(\frac { 1 }{ 10010 }\)
(d) \(\frac { 1 }{ 10001 }\)
Solution:
(b) \(\frac { 1 }{ 10100}\)
Hint:

Question 10.
The value of \(\int_{0}^{π}\) \(\frac { dx }{ 1+5^{cosx} }\) is
(a) \(\frac { π }{ 2 }\)
(b) π
(c) \(\frac { 3π }{ 2 }\)
(d) 2π
Solution:
(a) \(\frac { π }{ 2 }\)
Hint:

Adding (1) and (2)

Question 11.
If \(\frac { Γ(n+2) }{ Γn }\) = 90 then n is
(a) 10
(b) 5
(c) 8
(d) 9
Solution:
(d) 9
Hint:

n² + n = 90
n² + n – 90 = 0
(n + 10) (n – 9) = 0
n = 9

Question 12.
The value of \(\int_{0}^{π/6}\) cos³ 3x dx is
(a) \(\frac { 2 }{ 3 }\)
(b) \(\frac { 2 }{ 9}\)
(c) \(\frac { 1 }{ 9 }\)
(d) \(\frac { 1 }{ 3 }\)
Solution:
(b) \(\frac { 1 }{ 10100}\)
Hint:
\(\int_{0}^{π/6}\) cos³ 3xdx = \(\frac { 1 }{ 3 }\) × \(\frac { 2 }{ 3 }\) × 1
= \(\frac { 2 }{ 9 }\)

Question 13.
The value of \(\int_{0}^{π}\) sin⁴ x dx
(a) \(\frac { 3π }{ 10 }\)
(b) \(\frac { 3π }{ 8}\)
(c) \(\frac { 3π }{ 4 }\)
(d) \(\frac { 3π }{ 2 }\)
Solution:
(b) \(\frac { 3π }{ 8}\)
Hint:
(x) = sin⁴x dx
f(π – x) = sin⁴ (π – x) = sin⁴x

Question 14.
The value of \(\int_{0}^{∞}\) e^-3x x² dx
(a) \(\frac { 7 }{ 27 }\)
(b) \(\frac { 5 }{ 27 }\)
(c) \(\frac { 4 }{ 27 }\)
(d) \(\frac { 2 }{ 27 }\)
Solution:
(d) \(\frac { 2 }{ 27 }\)
Hint:

Question 15.
If \(\int_{0}^{a}\) \(\frac { 1 }{ 4+x^2 }\) dx = \(\frac { π }{ 8 }\) then a is
(a) 4
(b) 1
(c) 3
(d) 2
Solution:
(d) 2
Hint:

Question 16.
The volume of solid of revolution of the region bounded by y² = x(a – x) about the x-axis is
(a) πa³
(b) \(\frac { πa^3 }{ 4 }\)
(c) \(\frac { πa^3 }{ 5 }\)
(d) \(\frac { πa^3 }{ 6 }\)
Solution:
(d) \(\frac { πa^3 }{ 6 }\)
Hint:
y² = x(a – x)
To find limit put y = 0
x (a – x) = 0
x = 0, x = a

Question 17.
If f(x) = \(\int_{1}^{x}\) \(\frac { e^{sinx} }{ u }\) du, x > 1 and \(\int_{1}^{3}\) \(\frac { e^{sinx^2} }{ x }\) dx = \(\frac { πa^3 }{ 6 }\) [f(a) – f(1)] then one of the possible value of a is
(a) 3
(b) 6
(c) 9
(d) 5
Solution:
(c) 9
Hint:

Question 18.
The value of \(\int_{0}^{1}\) (sin^-1 x)² dx is
(a) \(\frac { π^2 }{ 4 }\) – 1
(b) \(\frac { π^2 }{ 4 }\) + 2
(c) \(\frac { π^2 }{ 4 }\) + 1
(d) \(\frac { π^2 }{ 4 }\) – 2
Solution:
(d) \(\frac { π^2 }{ 4 }\) – 2
Hint:

Question 19.
The value of \(\int_{0}^{a}\) (\(\sqrt{a^2-x^2}\))³ dx is
(a) \(\frac { πa^3 }{ 16 }\)
(b) \(\frac { 3πa^4 }{ 16 }\)
(c) \(\frac { 3πa^2 }{ 8 }\)
(d) \(\frac { 3πa^4 }{ 8 }\)
Solution:
(b) \(\frac { 3πa^4 }{ 16 }\)
Hint:

Question 20.
If \(\int_{0}^{x}\) f(t) dt = x + \(\int_{x}^{1}\) f(t) dt, then the value of f(1) is
(a) \(\frac { 1 }{ 2 }\)
(b) 2
(c) 1
(d) \(\frac { 3 }{ 4 }\)
Solution:
(a) \(\frac { 1 }{ 2 }\)
Hint:

= 1 + 0 – x f(x)
f(x) + x f(x) = 1
f(x)[1 + x] = 1
when x = 1,
f(1)(2) = 1
f(1) = \(\frac { 1 }{ 2 }\)

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Accountancy Guide Pdf Chapter 6 Retirement and Death of a Partner Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Accountancy Solutions Chapter 6 Retirement and Death of a Partner

12th Accountancy Guide Retirement and Death of a Partner Text Book Back Questions and Answers

I Multiple Choice Questions

Choose the correct answer

Question 1.
A partner retires from the partnership firm on 30th June. He is liable for all the acts of the firm up to the
(a) End of the current accounting period
(b) End of the previous accounting period
(c) Date of his retirement
(d) Date of his final settlement
Answer:
(c) Date of his retirement

Question 2.
On the retirement of a partner from a partnership firm, accumulated profits and losses are distributed to the partners on the basis of
(a) New profit sharing ratio
(b) Old profit sharing ratio
(c) Gaming ratio
(d) Sacrificing ratio
Answer:
(b) Old profit sharing ratio

Question 3.
On the retirement of a partner, general reserve will be transferred to the
(a) Capital account of all the partners
(b) Revaluation account
(c) Capital account of the continuing partners
(d) Memorandum revaluation account
Answer:
(a) Capital account of all the partners

Question 4.
On revaluation, the increase in liabilities leads to ……………….
(a) Gain
(b) Loss
(c) Profit
(d) None of these
Answer:
(b) Loss

Question 5.
At the time of retirement of a partner, determination of gaining ratio is required
(a) To transfer revaluation profit or loss
(b) To distribute accumulated profits and losses .
(c) To adjust goodwill
(d) None of these
Answer:
(c) To adjust goodwill

Question 6.
The final amount due to a retiring partner is not paid immediately,it is transferred to
(a) BankA/c
(b) Retiring partners capital A/c
(c) Retiring partner s loan A/c
(d) Other partner s capital A/c
Answer:
(c) Retiring partner s loan A/c

Question 7.
‘A’was a partner in a partnership firm. He died on 31st March 2019. The final amount due to him is ? 24,000 which is not paid immediately. It will be.transferred to
(a) As capital account
(b) A’s loan account
(c) As Executors account
(d) As Executors loan account
Answer:
(d) As Executors loan account

Question 8.
A, B and C are partners sharingprofits in the ratio of 2:2:1. On retirement of B, goodwill of the firm was valued as ₹ 30,000. Find the contribution of A and C to compensate B:
(a) ₹ 20,000 and ₹ 10,000
(b) ₹ 8,000 and ₹ 4,000
(c) ₹ 10,000 and ₹ 20,000
(d) ₹ 15,000 and ₹ 15,000
Hint:

∴ Retire partner share will be compensate of‘A’ and ‘Copartners
’A’ Goodwill value = 30,000 x \(\frac{2}{5}\) = 5 12,000
‘B’ Goodwill Value = 30,000 x \(\frac{2}{5}\) = 5 12,000
‘C’ Goodwill Value = 30,000 x \(\frac{1}{5}\) = 5 6,000
Now Compensate A& C
‘B’ Share good will – 12,000 x \(\frac{2}{3}\) = 8,000
12,000 x \(\frac{1}{3}\) = 4,000
Answer:
(b) ₹ 8,000 and ₹ 4,000

Question 9.
A, B and C are partners sharing profits in the ratio of 4:2:3. C retires. The new profit sharing ratio between A and B will be
(a) 4:3
(b) 3:4
(c) 2:1
(d) 1:2
Hint:
OldPartnersABC

Answer:
(c) 2:1

Question 10.
X, Y and Z were partners sharing profits and losses equally. X died on 1st April 2019. Find out the share of X in the profit of 2019 based on the profit of 2018 which showed ₹ 36,000.
(a) ₹ 1,000
(b) ₹ 3,000
(c) ₹ 12,000
(d) ₹ 36,000
Hint:
Partner’s X: Y: Z
Sharing ratio = equally =\(\frac{1}{3}: \frac{1}{3}: \frac{1}{3}\)
Profit = ₹ 36,000
Share of ‘X’
36,000 x \(\frac{1}{3}\) = ₹ 12,000
Answer:
(c) ₹ 12,000

II Very Short Answer Questions

Question 1.
What is meant by the retirement of a partner?
Answer:
When a partner leaves from partnership firm it is known as retirement. The reasons for the retirement of a partner may be illness, old age, and disagreement with other partners, etc.

Question 2.
What is the gaining ratio?
Answer:
The continuing partners may gain a portion of the share of profit of the retiring partner. The gain may be shared by all the partners or some of the partners. The gaining ratio is the proportion of the profit which is gained by the continuing partners.

Question 3.
What is the purpose of calculating the gaining ratio?
Answer:
The purpose of finding the gaining ratio is to bear the goodwill to be paid to the retiring partner.

Question 4.
What Is the journal entry to be passed to transfer the amount due to the deceased partner to the executor of the deceased partner?
Answer:
To transfer the amount due to the deceased partner to the executor or legal representative of the deceased partner.

III. Short Answer Questions

Question 1.
List out the adjustments made at the time of retirement.
Answer:
The Following adjustments are necessary at the time of retirement of a partner:

• Distribution of accumulated profits, reserves, and losses
• Revaluation of assets and liabilities
• Determination of new profit sharing ratio and gaining ratio
• Adjustment for goodwill
• Adjustment for current year’s profit or loss up to the date of retirement
• Settlement of the amount due to the retiring partner

Question 2.
Distinguish between sacrificing ratio and gaining ratio.
Answer:

Question 3.
What are the ways in which the final amount to an outgoing partner can be settled?
Answer:
The amount due to the retiring partner may be settled one of the following ways:

1. Paying the entire amount due immediately in cash
2. Transfer the entire amount due to the loan account of the partner
3. Paying part of the amount immediately in cash and transferring the balance to the loan account of the partner.

IV Exercise

Distribution of accumulated profits, reserves, and losses

Question 1.
Dheena, Surya, and Jankai are partners sharing profits and losses in the ratio of 5:3:2. on 31.3.2018, Dheena retired. On the date of retirement, the books of the firm showed a reserve fund of ₹ 50,000. The pass journal entry to transfer the reserve fund.
Solution:

Answer:
Reserves fund: dheena: ? 25,000(Cr); Surya: ₹ 15,000(Cr.); Janaki: ₹ 10,000(Cr.);

Question 2.
Rosi, Rathi, and Rani are partners of firms sharing profits and losses equally. Rathi retired from the partnership on 1.1.2018. On the date, their balance sheet showed an accumulated loss of ₹ 45,000 on the asset side of the balance sheet. Give the journal [ entry to distribute the accumulated loss.
Solution:

Answer:
Rosi: ₹ 15,000(Dr.); Rathi: ₹ 15,000(Dr.);Rani: ₹ 15,000(Dr.);

Question 3.
Akash, Mukesh, and Sanjay are partners in firm sharing profits and losses in the ratio of 3:2:1. Their balance sheet as on 31st March 2017 is as follows:

Pass journal entry to transfer the accumulated profit and prepare the capital account of the partners
Solution:


Answer:
Akash capital: ₹ 67,000(Cr.); Mugesh Capital: ₹ 78,000(Cr.); Sanjay’s Capital:₹ 39,000(Cr.);

Question 4.
Roja, Neeia ‘and Kanaga are partners, sharing profit and losses in the ratio of 4:3:3. On 1st April 2017, Roja retires and on retirement, the following adjustments are agreed upon.
(i) Increase the value of the Building by ₹ 30,000.
(ii) Depreciate stock by ₹ 5,000, and furniture by ₹ 12,000.
(iii) Provide for an outstanding liability of ₹ 1,000.
Pass journal entries and prepare revaluation account.
Solution:

Answer:
Revaluation profit : ₹ 12,000

Question 5.
Vinoth, Karthi, and Pranav are partners sharing profits and. losses’ in the ratio of 2:2:1 Pranav retires from the partnership on 1st April 2018. The following adjustments are to be made.
(i) increase the value of the land building by ₹ 18,000.
(ii) Reduce the value of machinery by ₹ 15,000.
(iii) A provision would also be made for outstanding expenses for ₹ 8,000.
Give journal entries and prepare a revaluation account.
Solution:

Question 6
Chandru, Vishal, and Ramanan are partners in firms sharing profits and losses equally. Their balance sheet as of 31st March 2018 is as follows.

Ramanan retired on 31st March 2019 subject to the following conditions:
(i) Machinery is valued at ₹ 1,50,000
(ii) Value of furniture brought down by ₹ 10,000
(iii) Provision for doubtful debts should be increased to ₹ 5,000. ,
(iv) investment of ₹ 30,000 not recorded in the books is to be recorded now.
Pass necessary journal entries and prepare revaluation account and capital account of partners.
Solution:

Answer:
Revaluation profit: ₹ 48,000;
Capital account:)
Chandru :₹ 76,000(Cr);
Vishal: ₹ 86,000(Cr);
Ramanan’s loan account: ₹ 86,000 (a))

Question 7.
Kayal, Mala and Neela are partners sharing profits in the ratio of 2:2:1. kayal retires and the new profit sharing ratio between Mala and Neela is 3:2. Calculate the gaining ratio.
Solution:
New Profit Sharing Ratio and Gaining Ratio
Gain Ratio = New Ratio – Old Ratio
Kayal –
Mala = \(\frac { 3 }{ 2 }\) – \(\frac { 2 }{ 5 }\) – \(\frac { 1 }{ 5 }\)
Neela = \(\frac { 2 }{ 5 }\) – \(\frac { 1 }{ 5}\) = \(\frac { 1 }{ 5 }\)
Gaining Ratio = 1:1

Question 8.
Sunil, Sumathi and Sundari are partners sharing profits in the ratio of 3:3:4. Sundari retires and her share is taken up entirely by Sunil. Calculate the new profit sharing ratio and gaining ratio.
Solution:
old ratio = 3:3:4 (Sunil:sumathi:sundar)
New Ratio = old ratio + gaining ratio

Answer:
Gaining ratio:4:0;
New ratio:7:3

Question 9.
Ramu, Somu and Gopu are partners sharing profits in the ratio of 3:5:7. Gopu retires and the share is purchased by Ramu and Somu in the ratio of 3:1. Find the new profit sharing ratio and gaining ratio.
Solution:

Question 10.
Navin, Ravi and Kumar are partners sharing profits in the ratio of 1/2, 1/4 and 1/4 respectively. Kumar retires and his share is taken up by Navin and Ravi equally. Calculate the new profit sharing ratio and gaining ratio.
Solution :

Answer:
New ratio:5:3;
Gaining ratio: 1:1

Question 11.
Mani, Gani and Soni are partners sharing the profits and losses in the ratio of 4:5:6. Mani retires from the firm. Calculate the new profit sharing ratio and gaining ratio.
Mani: Gani: Soni → 4:5:6
[If nothing is mentioned about the new ratio, old ratio of the continuing partners is equal to their new ratio.]
Solution:
Old ratio = 4:5:6
New ratio – 5:6

Answer:
New profit shaving ratio and gaining ratio is 5:6

Question 12.
Rajan, Suman and jegan were partners in firm sharing profits and losses in the ratio of 4:3:2 Suman retired from partnership. The goodwill of the firm on the date of retirement was valued at ₹ 45,000. Pass necessary journal entries for goodwill on the assumption that the fluctuating capital method is followed.
Solution :

Answer:
Suman’s share of goodwill: ₹ 15,000;
Rajan’s capital: ₹ 10,000(Dr);Jegan’s capital: ₹ 5,000(Dr);

Question 13.
Balu, Chandru and Nirmal are partners in a firm sharing profits and losses in the ratio of 5:3:2 on 31st March 2018, Nirmal retires from the firm. On the date of Nirmal’s retirement, goodwill appeared in the books of the firm at ₹ 60,000 By assuming thuctuating capital account, pass the necessary journal entry if the partners decide to
(a) Write off the entire amount of existing goodwill
(b) Write off half of the existing goodwill.
Solution :

Answer:
(a) Balu’s capital: ₹ 30,000(Dr.); Chandru’s capital: ₹ 18,000(Dr.)
Nirmala’s capital: ₹ 12,000(Dr);(b)balu’s capital: ₹ 15,000(Dr);
Chandru’s capital: ₹ 9,000(Dr);Nirmala’s capital: ₹ 6,000(Dr);

Question 14.
Rani, Jaya and Rathi are partners sharing profits and losses in the ratio of 2:2:1. On 31.3.2018, Rathi retired from the partnership. Profit of the preceding years is as follows: 2014: ₹ 10,000; 2015; ₹ 20,000; 2016; ₹ 18,000 and 2017; ₹ 32,000
Find out the share of profit of Rathi for the year 2018 till the date of retirement if
(a) profit is to be distributed on the basis of the previous year’s profit
(b) Profit is to be distributed on the basis of the average profit of the past 4 years.
Also pass necessary journal entries by assuming partners’ capitals are fluctuating.
Solution:
(a) on the basis of previous years profit
Profit of 2017 = Rs.32,000
Date of retirement = 31.3.2018
share of profit of Rathi for 3 months = \(32,000 \times \frac{3}{12} \times \frac{1}{5}\)
= Rs. 1600

Answer:
(a) Rathi’s share of profit: ₹ 1,600; (b) Rathi’s share of profit: ₹ 1,000;
Settlement of amount due to the retiring partner.

Question 15.
Kavin, Madhan, and Ranjith are partners sharing profits and losses in the ratio of 4:3:3 respectively. Kavin retires from the firm on 31st December 2018. On the date of retirement, his capital account shows a credit balance of ₹ 1,50,000. Pass journal entries if:
(a) The amount due is paid off immediately.
(b) The amount due is not paid immediately.
(c) ₹ 1,00,000 is paid and the balance in the future.
Solution:

Answer:
(a) Kavin’s loan:Nil;
(b) Kavin’s loan: ₹ 1,50,000;
(c) Kavin’s loan: ₹ 50,000;

Question 16.
Manju, Chara’and Lavanya are partners in firm sharing profits and losses in the ratio of 5:3:2. The balance sheet as of 31st March, 2018 was as follows:

Manju retired from the partnership firm on 31.3.2018 subject to the following adjustments:
(i) Stock to be depreciated by ₹ 10,000
(ii) Provision for doubtful debts to be created for ₹ 3,000
(iii) Buildings to be appreciated by ₹ 28,000.
Prepare revaluation account and capital accounts of partners after retirement.
Solution:

Answer:
Revaluation profit: ₹ 15,000; Manju’s loan account:
₹ 1,02,000(Cr).Capital account: Charu ₹ 89,OO0(Cr); Lavanya: ₹ 83,000(Cr))

Question 17.
Kannan, Rahim, and John are partners in a firm sharing profits and losses in the ratio of 5:3:2. The balance sheet as of 31st December 2017 was as follows:

John retires on 1st January 2018, subject to the following conditions :
(i) To appreciate building by 10%
(ii) Stock to be depreciated by 5%
(iii) To provide ₹ 1,000 for bad debts
(iv) An unrecorded liability of ₹ 8,000 has been noticed.
(v) The retiring partner shall be paid immediately.
prepare revaluation account, partner’s capital account, and the balance sheet of the firm after retirement.
Solution :

Answer:
Revaluation loss: ₹ 1,000; capital Account; Kannan: ₹ 1,04,500
Rahim: ₹ 82,700 Amount paid to John ₹ 41,800; Balance sheet total: ₹ 2,15,000

Question 18.
Saran, Arun, and Karan are partners in firms sharing profits and losses in the ratio of 4:3:3. The balance sheet as of 31.12.2016 was as follows:

Karan retires on 1.1.2017, subject to the following conditions:
(i) Goodwill of the firm is valued at ₹ 21,000 %
(ii) Machinery to be appreciated by 10%
(iii) Building to be valued at ₹ 80,000
(iv) provision for bad debts to be raised to ₹ 2,000
(v) Stock to be depreciated by ₹ 2,000
(vi) The final amount due to Karan is not paid immediately.
prepare the necessary ledger accounts and show the balance sheet of the firm after retirement. *
Solution:

Gaining ratio
Old ratio = 4:3:3
New ratio = 4:3
Gaining ratio = Saran = New ratio – old ratio

GR = 12:9 or 4:3
Karan’s share of G/w = 21,000 x \(\frac{3}{10}\) = Rs.6,300
K’s g/w In GR = Rs. 6,300
Saran’s share = 6300 x \(\frac{3}{10}\) = Rs.3,600
Aruns share = 6,300 x \(\frac{3}{7}\) = Rs.2,700
Answer:
Revaluation profit: ₹ 21,000; capital A/c: Saran: ₹ 70,800, Arun: ₹ 58,100
Karan’s loan Account ₹ 57,100; Balance sheet total: ₹ 2,21,000

Question 19.
Rajesh, Sathish and Mathan are partners sharing profits and losses in the ratio of 3:2:1. respectively. Their balance sheet as on 31.3.2017 is given below:

Mathan retires on 31st March, 2017 subject to the following conditions :
(i) Rajesh and Sathis will share profits and losses in the ratio of 3:2
(ii) Assets are to be revalued as follows;
Machinery ₹ 4,50,000, Stock ₹ 2,90,000 , Debtors ₹ 1,52,000
(iii) Goodwill of the firm is valued at ₹ 1,20,000
prepare the necessary ledger accounts and the balance sheet immediately after the retirement of Mathan.
Solution:

Gaining ratio = New ratio – old ratio
Rajesh = \(\frac{3}{5}-\frac{3}{6}=\frac{18-15}{30}=\frac{3}{30}\)
Sathish = \(\frac{2}{5}-\frac{2}{6}=\frac{12-10}{30}=\frac{2}{30}\)
GR = 3:2
Mathans share of G/w = 12,000 x \(\frac{1}{6}\) = Rs.20,000
In gaining ratio
Rajeshs share = 20,000 x \(\frac{3}{5}\) = Rs. 12,000
Sathishs share = 12,000 x \(\frac{2}{5}\) = Rs. 8,000

Answer:
Revaluation Profit: ₹ 12,000; Mathan loan: A/c: ₹ 2,92,000 Rajesh’s capital A/c ₹ 4,54,000; Sathish capital A/c: ₹ 3,36,000
Balance sheet total ₹ 13,10,000

Question 20.
Janani and Jamuna are partners sharing profits and losses in the ratio of 3:3:1. respectively. Janaki died on 31st December 2017. The final amount due to her showed a credit balance of ₹ 1,40,000. Pass Journal Entry if
(i) The amount due is paid off immediately.
(ii) The amount due is not paid immediately.
(iii) ₹ 75,000 is paid and the balance in the future.
Solution:

Question 21.
Varsha, Shanthi, and Madhuri are partners in a firm sharing profits in the ratio of 5:4:3. Their balance sheet as of 31st December 2017 is as under:

on 1st January 2018, Madhuri died and on her death, the following arrangements are made:
(i) Stock to be depreciated by ₹ 5,000
(ii) Premises is to be appreciated by 20%
(iii) To provide ₹ 4,000 for bad debts
(iv) The final amount due to Madhuri was not paid.
prepare revaluation account, partners capital account, and the balance sheet of the firm after death.
Solution:

Answer: Revaluation Profit ₹ 15,000;
Varsha’s capital A/c ₹ 1,01,250; Sathish capital A/c: ₹ 77,000
Madhuri’s executors account ₹ 32,750; Balance sheet total: ₹ 2,43,000

Question 22.
Vijayan, Sudhan, and Suman are partners who share profits and losses; in the capital ratio. Their balance sheet as of 31st December 2018 is as follows:

Suman died on 31.3.2019. On the death of Suman, the following adjustments are made:
(i) Building is to be valued at ₹ 1,00,000
(ii) Stock to be depreciated by ₹ 5,000
(iii) Goodwill of the firm is valued at ₹ 36,000
(iv) Share of profit from the closing of the last financial year to the date of death on the basis of the average of the three completed year’s profit before death.
profit for 2016, 2017 and 2018 were ₹ 40,000,₹ 50,000 and ₹ 30,000 respectively.
Prepare the necessary ledger accounts and the balance sheet immediately after the death of Suman.
Solution:

Suman share of G/w
Vijayan : Sudhan : suman
Old ratio = 7:5:3
New ratio = 7:5
Gaining ratio New ratio – old ratio

Answer:
Revaluation Profit: ₹ 15,000; Vijayan’s capital A/c: ₹ 81,200;
Sudhan’s capital A/c ₹ 58,000; Suman’s Executor’s A/c: ₹ 45,800
Balance sheet total: ₹ 2,02,000

12th Accountancy Guide Retirement and Death of a Partner Additional Important Questions and Answers

I. Choose the best answer

Question 1.
In the absence of any specific agreement, between the partners, partners loan to the firms will carry an inters at the rate of …………… %
(a) 5%
(b) 6%
(c) 4%
Answer:
(b) 6%

Question 2.
A,B & C shares profit as 1/2 to A, 1/3 to B, and 1/6 to C. If B retries, then the new profit sharing ratio ………..
(a) 3:1
(b) 3:2
(c) 1:3
Hint:
Old Partner’s A, B, C
Old ratio = \(\frac{1}{2}: \frac{1}{3}: \frac{1}{6}\)
‘B’ Retire Partner
In order to equalise the denomination
\(\frac{3}{6}: \frac{2}{3}: \frac{1}{6}\)
Now profit sharing ration = \(\frac{3}{4}: \frac{1}{4}\). or 3 :1
Answer:
(a) 3:1

Question 3.
At the time of retirement, the revelation profits of the business will be shared by ……………… partners.
(a) all the partners
(b) Continuing partners
(c) Old partners
Answer:
(a) all the partners

Question 4.
At the time of retirement, of partners, the existing partners stand to
(a) gain
(b) loss
(c) no change
Answer:
(a) gain

Question 5.
A,B & C are sharing profits in the ratio of \(\frac{2}{5}\) , \(\frac{2}{5}\) \(\frac{1}{5}\) C retired from business and his share was purchased equally by A and B, Then new profit sharing ratio shall be

Hint:

Answer:
a

Question 6.
If the amount due to the outgoing partner is transferred to loan A/c then he is entitled to interest at ……………….. until it is paid out.
(a) 6%
(b) 5%
(c) 8%
Answer:
(a) 6%

Question 7.
At the time of retirement of a partner calculation of new profit, ratio is
(a) not necessary
(b) necessary
(c) optional
Answer:
(b) necessary

III Short Answer Questions

Question 1.
What are the journal entries to be passed to transfer the accumulated profits, losses & reserves?
Answer:

Question 2.
Write the format of Revaluation A/c.
Answer:
New profit sharing ratio is the agreed proportion in which future profit will be distributed to the continuing partners. If the new profit sharing ratio is not agreed, the continuing partners will share the profits and losses equally.

Question 3.
How will you adjust the share of profits loss of the retaining partner if he retires in between in an accounting year?
Answer:
When a partner retires in between in an accounting year, his share of the current year’s profit or loss upto the date of retirement has to be distributed to the retiring partner. It may be estimated based on the current year’s turnover. The previous year’s profit or the average of the past year’s profit may also be taken as the base to estimate the current year’s profit. The following journal entry is passed

Question 4.
What are the adjustments to be made on the death of a partner?
Answer:
The following adjustments are made on the death of a partner.

• Distribution of accumulated profits, reserves, and losses
• Revaluation of assets and liabilities
• Determination of new profit sharing ratio and gaining ratio
• Adjustment for goodwill
• Adjustment for current year’s profit or loss upto the date of death
• Settlement of the amount due to the deceased partner.

Question 5.
What are the journal entries to be passed for settlement of the amount due to the deceased partner
Answer:
To transfer the amount due to the deceased partner to the executor or legal representative of the deceased partner.

IV Additional Problems:

Question 1.
A, B, and C sharing profits in the ratio of 5:3:2. C retires. Find out the new profit sharing ratio and gaining ratio.
Solution:

Question 2.
G, H, and I are partners sharing profits in the ratio of 5:3:2.1 taken up by G and H equally. Find out the new profit sharing ratio of G and H.
Solution:

Question 3.
J, K and L are partners sharing profits in the ratio of 5:3:2. retires and his share was taken up entirely by K. Find out the new profit sharing ratio and gaining ratio of continuing partners
Solution:

Question 4.
X,Y and Z are partners sharing profits in- the ratio of 5:3:2 Z retires and the ratio between X and Y is 3:2. Find out the gaining ratio
Solution :

Question 5.
Prabha,Kavitha and Meena were partners of a firm sharing profit and loss in the ratio of 3:2:1 Meena Wanted to retire. They decided to revalue the assets and liabilities of the firm as indicated below:
To write down Machinery by Rs 10,000 and Stock by Rs. 4,000
To bring into books as unrecorded investments Rs. 5,000
To Write off Rs.3,000 from sundry creditors as it was no longer liable.
Pass entries to give effect to the above adjustments. Show also Revaluation account.
Solution:

Question 6.
Banumathi, Bharafhi and Shanthi are partners sharing, profits in the ratio of 5:3:2. On April 1, 2005 Shanthi decided to retire. On that date, there was a credit balance of Rs. 60,000 in their profit and loss account. Pass entry.
Solution:

Question 7.
Thangamuthu, Anaimuthu and Vairamuthu are partners sharing profit and loss in the ratio of 3:3:2. Thangamuthu wanted to retire on 1st June 2005, the firms books showed a general reserve of Rs. 40,000. Pass entry.
Solution:

Question 8.
Lalitha, Jothi and Kanaga were partners of a sharing profit and losses in the ratio of 3:2:3, Set out below was their balance sheet as on 31st March 2003.

Lalitha retired from the partnership on 1st April 2004 on the following terms:
Goodwill of the firm was to be valued at Rs.30,000
The assets are to be valued as under Stock Rs. 1,00,000; Furniture Rs.15,000; Plant and Machinery Rs.45,000; Building Rs.1,00,000.
A provision for doubtful debts is created at Rs.4,250.
Lalitha was to be paid off immediately.
Show the journal entries, prepare a revaluation account, capital account, Bank account, and balance sheet of the reconstituted partnership.
Solution:

Question 9.
‘9. A, B and C are partners sharing profits and losses in the ration of 5:3:2 respectively. Retries from the firm on 1st April 2005. After his retirement, his capital account shows a credit balance of Rs.1,35,000 after the necessary adjustment made. Give journal entries, if.
the amount due is paid off immediately.
When the amount due is not paid immediately.
Rs. 45,000 is paid and the balance In the future.
Solution :

Question 10.
Pallavan, Pandian and Chozhan were carrying on partnership business sharing profits in the ratio of 3:2:1. On March 31, 2005, the balance sheet of the firm stood as follows:

Chozhan retried on April 1, 2005 on the following terms:
Building to be appreciated by Rs. 15,000
Provision for doubtful debts to be made at 6% on debtors
Goodwill of the firm is valued at Rs. 18,000
Rs.50,000 to be paid to chozhan immediately and the balance transferred to his loan account.
Prepare Revaluation Account, Capital Accounts, Bank Account and the Balance Sheet after Chozhan’s retirement.
Solution :

Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 12 Introduction to Probability Theory Ex 12.5 Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 12 Introduction to Probability Theory Ex 12.5

Choose the correct or most suitable answer from the given four alternatives

Question 1.
Four persons are selected at random from a group of 3 men, 2 women and 4 children. The probability that exactly two of them are children is
(1) \(\frac{3}{4}\)
(2) \(\frac{10}{23}\)
(3) \(\frac{1}{2}\)
(4) \(\frac{10}{21}\)
Answer:
(4) \(\frac{10}{21}\)

Explaination:
Number of Men = 3
Number of Women = 2
Number of Children = 4
Number of ways of choosing 2 children out of 4 children = 4C₂
= \(\frac{4 \times 3}{1 \times 2}\) = 6
Number of ways of choosing 4 persons from total 9 persons = 9C₄

= 9 × 2 × 7
= 126
Number of ways of choosing 2 persons (other than 2 children) from the remaining 5 persons (excluding children) = 5C₂

Probability that exactly two of them are children

Question 2.
A number is selected from the set (1, 2, 3, ….., 20}. The probability that the selected number is divisible by 3 or 4 is
(1) \(\frac{2}{5}\)
(2) \(\frac{1}{5}\)
(3) \(\frac{2}{5}\)
(4) \(\frac{2}{5}\)
Answer:
(3) \(\frac{2}{5}\)

Explaination:
Sample space S is
S = {1, 2, 3, ………. , 20}
n(S) = 20
Let A be the event of selecting a number divisible by 3
A = {3, 6, 9, 12, 15, 18}
n(A) = 6
Let B be the event of selecting a number divisible by 4
B = {4, 8, 12, 16, 20}
n(B) = 5
A ∩ B = {12}
n(A ∩ B) = 1
P (Number divisible by 3 or 4) = P (A ∪ B)
= P(A) + P(B) – P(A ∩ B)

Question 3.
A, B and C try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are \(\frac{3}{4}\), \(\frac{1}{2}\), \(\frac{5}{8}\). The probability that the target is hit by A or B but not by C is
(1) \(\frac{21}{64}\)
(2) \(\frac{7}{32}\)
(3) \(\frac{9}{64}\)
(4) \(\frac{7}{8}\)
Answer:
(1) \(\frac{21}{64}\)

Explaination:
Given Probability of hitting the target by A is P(A) = \(\frac{3}{4}\)
Probability of hitting the target by B is P(B) = \(\frac{1}{2}\)
Probability of hitting the target by C is P(C) = \(\frac{5}{8}\)
Given A, B , C are Independent.
∴ P(A ∩ B ∩C) = P(A) P(B) . P(C)
Probability of the target hit by A or B but not by C is
P(A ∩ B ∩ C̅) = P(A ∪ B) . P(C̅)
= [P(A) + P(B) – P (A ∩ B)] [1 – P(C)]
= [P(A) + P(B) – P(A) P(B)] [1 – P(C)]

Question 4.
If A and B are any two events, then the probability that exactly one of them occur is
(1 P(A ∪ B̅) + P(A̅ ∪ B)
(2) P(A ∩ B̅) + P(A̅ ∩ B)
(3) P(A) + P(B) – P(A ∩ B)
(4) P(A) + P(B) + 2P(A ∩ B)
Answer:
(2) P(A ∩ B̅) + P(A̅ ∩ B)

Explaination:
Let A and B be an two events
The probability that exactly one of them occur is
= P(A ∩ B̅) + P(A̅ ∩ B)

Question 5.
Let A and B be two events such that\(\)
P\((\overline{\mathbf{A} \cup \mathbf{B}})\) = \(\frac{1}{6}\), P(A ∩ B) = \(\frac{1}{4}\) and P(A̅) = \(\frac{1}{4}\)
Then the events A and B are
(1) Equally likely but not independent
(2) Independent but not equally likely
(3) Independent and equally likely
(4) Mutually inclusive and dependent
Answer:
(2) Independent but not equally likely

Explaination:


If P(A ∩ B) = p(A) . p(B), then A and B are independent.
we have (A ∩ B) = \(\frac{1}{4}\) ………… (1)
P(A) . P(B) = \(\frac{3}{4} \times \frac{1}{3}=\frac{1}{4}\) ………… (2)
From equations (1) and (2) we get
P(A ∩ B) = p(A) . p(B)
∴ A and B are independent
Since P(A) ≠ P(B), not equally likely.
∴ A and B are independent but not equally likely.

Question 6.
Two items are chosen from a lot containing twelve items of which four are defective, then the probability that at least one of the item is defective
(1) \(\frac{19}{33}\)
(2) \(\frac{17}{33}\)
(3) \(\frac{23}{33}\)
(4) \(\frac{13}{33}\)
Answer:
(1) \(\frac{19}{33}\)

Explaination:
Total number of items = 12
Number of ways of choosing two items from 12 items is = 12C₂
Number of defective items = 4
Number of non defective items = 8
Probability of getting atleast one defective items

Question 7.
A man has 3 fifty rupee notes, 4 hundred rupees notes and 6 five hundred rupees flotes in his pocket. If 2 notes are taken at random, what are the odds in favour of both notes being of hundred rupee denomination?
(1) 1 : 12
(2) 12 : 1
(3) 13 : 1
(4) 1 : 3
Answer:
(1) 1 : 12

Explaination:
Let S be the sample space and A be the event of taking 2 hundred rupee notes.
n(S) = 13C₂ = \(\frac{13 \times 12}{1 \times 2}\) = 13 × 6
n(S) = 78
n(A) = 4C₂ = \(\frac{4 \times 3}{1 \times 2}\) = 2 × 3
n(A) = 6
n(A̅) = n(S) – n(A)
= 78 – 6 = 72
∴ Odds in favour of A is 6 : 72
That is 1 : 12

Question 8.
A letter is taken at random from the letters of the word ‘ASSISTAN’T’ and another letter is taken at random from the letters of the word ‘STATISTICS’. The probability that the selected letters are the same is
(1) \(\frac{7}{45}\)
(2) \(\frac{17}{90}\)
(3) \(\frac{29}{90}\)
(4) \(\frac{19}{90}\)
Answer:
(4) \(\frac{19}{90}\)

Explaination:
Given words ‘ASSISTANT’ ‘STATISTICS
Sample space S = {(A, S, S, I, S, T, A, N, T)
(S,T, A, T, I, S, T, I, C, S)}
n(S) = {(A, S), (A, T), (A, A), (A, T), (A, I), (A, S), (A, T), (A, I), (A, C), (A, S) }
n(S) = 9 × 10 = 90
Let A be the event of se}ecting equal letters.
A = {(A, A), (A, A), (S, S), (S, S), (S, S), (S, S), (S, S), (S, S), (S, S), (S, S), (S, S), (1, 1), (1, 1), (T, T), (T,T) , (T, T), (T, T), (T, T), (T, T) }
n(A) = 19
Probability of getting equal letters = \(\frac{19}{90}\)

Question 9.
A matrix is chosen at random from a set of all matrices of order 2, with elements 0 or 1 only. The probability that the determinant of the matrix chosen is non zero will be
(1) \(\frac{3}{16}\)
(2) \(\frac{3}{8}\)
(3) \(\frac{1}{4}\)
(4) \(\frac{5}{8}\)
Answer:
(2) \(\frac{3}{8}\)

Explaination:
Sample space S = Set of all 2 × 2 matrices with elements 0 or 1 only
Number of elements in S is
n(S) = 2⁴ = 16
Let A be the event of getting 2 × 2 matrices with elements 0 or 1 only whose determinant is non zero.

Question 10.
A bag contains 5 white and 3 black balls. Five balls are drawn successively without replacement. The probability that they are alternately of different colours is
(1) \(\frac{3}{14}\)
(2) \(\frac{5}{14}\)
(3) \(\frac{1}{14}\)
(4) \(\frac{9}{14}\)
Answer:
(3) \(\frac{1}{14}\)

Explaination:
Number of White balls (W) = 5
Number of Black balls (B) = 3
Five balls are drawn successively without replacement.
Probability that they are alternately of different
colours = P (W B W B W) + P (BW BW B)
= P(W) . P(B) . P(W) . P(B) . P(W) + P(B) . P(W) . P(B) . P(W) . P(B)

Question 11.
If A and B are two events such that A ⊂ B and P(B) ≠ 0, then which of the following is correct?
(1) P(A/B) = \(\frac{\mathbf{P}(\mathbf{A})}{\mathbf{P}(\mathbf{B})}\)
(2) P(A/B) < P(A) (3) P(A/B) ≥ P(A) (4) P(A/B) >P(A)
Answer:
(3) P(A/B) ≥ P(A)

Explaination:
Given A and B are two events such that A ⊆ B
and P(B) ≠ 0 then
P(A/B) ≥ P(A)

Question 12.
A bag contains 6 green, 2 white , and 7 black balls. If two balls are drawn simultaneously, then the probability that both are different colours is
(1) \(\frac{68}{105}\)
(2) \(\frac{71}{105}\)
(3) \(\frac{64}{105}\)
(4) \(\frac{73}{105}\)
Answer:
(1) \(\frac{68}{105}\)

Explaination:
Number of green balls (G) = 6
Number of white balls (W) = 2
Number of black balls (B) = 7
Two balls are drawn simultaneously
P (Balls are of different colours)
= P[(GW or WG) or (WB or BW) or (BG or GB)]
= P(GW) + P(WG) + P(WB) + P(BW) + P(BG) + P(GB)
= P(G) P(W) + P(W) P(G) + P(W) P(B) + P(B) P(W) + P(B) P(G) + P(G) P(B)
= 2 [P(G) P(W) + P(W) P(B) + P(B) P(G)]

Question 13.
If X and Y be two events such that
P(X/Y) = \(\frac{1}{2}\), P(Y/X) = \(\frac{1}{3}\) and P( X ∩ Y) = \(\frac{1}{6}\),then
(1) \(\frac{1}{3}\)
(2) \(\frac{2}{5}\)
(3) \(\frac{1}{6}\)
(4) \(\frac{2}{3}\)
Answer:
(4) \(\frac{2}{3}\)

Explaination:

Question 14.
An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. The probability that the second ball drawn is red will be
(1) \(\frac{5}{12}\)
(2) \(\frac{1}{2}\)
(3) \(\frac{5}{12}\)
(4) \(\frac{5}{12}\)
Answer:
(2) \(\frac{1}{2}\)

Explaination:
Number of Red balls n (R) = 5
Number of Black halls n (B) = 5
Number of elements in the sample space n (S) = 5 + 5 = 10

Case (i)
P (drawing a red ball first) = \(\frac{5}{10}\)
Let P(E₁) = \(\frac{1}{2}\)
Now two red balls are added.
P (drawing a red ball after adding) = \(\frac{7}{12}\)
P(A/E₁) = \(\frac{7}{12}\)

Case (ii)
P (drawing a black ball first) = \(\frac{5}{10}\)
Let P(E₂) = \(\frac{1}{2}\)
Now two black halls are added.
P (drawing a black ball after adding) = \(\frac{5}{12}\)
P(A/E₂) = \(\frac{5}{12}\)
P(A) = P(A/E₁) . P(E₁) + P(A/E₂) . P(E₂)

Question 15.
A number x is chosen at random from the first 100 natural numbers. Let A be the event of numbers which satisfies \(\frac{(x-10)(x-50)}{x-30}\) ≥ 0 then P(A) is
(1) 0.20
(2) 0.51
(3) 0.71
(4) 0.70
Answer:
(3) 0.71

Explaination:
Given x is choosen from the first 100 natural numbers.
n(S) = 100

Satifies when x takes the values 31 to 100 and also at x = 10
∴ A = { 10, 31, 32, 33, ……………, 100}
n(A) = 71

Question 16.
If two events A and B are independent such that P(A) = 0.35 and P(A ∪ B) = 0.6, then P(B) is
(1) \(\frac{5}{13}\)
(2) \(\frac{1}{13}\)
(3) \(\frac{4}{13}\)
(4) \(\frac{7}{13}\)
Answer:
(1) \(\frac{5}{13}\)

Explaination:
Given A and B are independent events
P(A ∩ B) = P(A) P(B)
Also given P(A) = 0.35 and P(A ∪ B) = 0.6
P(A ∪ B) = P(A) – P(B) – P(A ∩ B)
P(A ∪ B) = P(A) + P(B) – P(A) . P(B)
0.6 = 0.35 + P(B) – 0.35 P(B)
0.6 = 0.35 + (1 – 0.35) P (B)
0.6 = 0.35 + 0.65 P (B)
0.65 P (B) = 0.6 – 0.35
P(B) = \(\frac{0.25}{0.65}\)
P(B) = \(\frac{25}{65}\) = \(\frac{5}{13}\)

Question 17.
If two events A and B are such that P(A̅) = \(\frac{3}{10}\) and P(A ∩ B̅) = \(\frac{1}{2}\) then P(A ∩ B) is
(1) \(\frac{1}{2}\)
(2) \(\frac{1}{3}\)
(3) \(\frac{1}{4}\)
(4) \(\frac{1}{5}\)
Answer:
(4) \(\frac{1}{5}\)

Explaination:

Question 18.
If A and B are two events such that P(B) = and P(B/A) = 0.6,then P(A̅ ∩ B) is
(1) 0.96
(2) 0.24
(3) 0.56
(4) 0.66
Answer:
(3) 0.56

Explaination:
Given A and B are two events.
P(A) = 0.4, P(B) = 0.8 and P(B/A) = 0.6

P (A ∩ B) = 0.6 × 0.4 = 0.24
P(A̅ ∩ B) = P(B) – P(A ∩ B)
= 0.8 – 0.24
P(A̅ ∩ B) = 0.56

Question 19.
There are three events A, B and C of which one and only one can happen. If the odds are 7 to 4 against A and 5 to 3 against B, then odds against C is
(1) 23 : 65
(2) 65 : 23
(3) 23 : 88
(4) 88 : 23
Answer:
(2) 65 : 23

Explaination:

Question 20.
If a and b are chosen randomly from the set {1, 2, 3, 4} with replacement, then the probability of the real roots of the equation x² + ax + b = 0
(1) \(\frac{3}{16}\)
(2) \(\frac{3}{16}\)
(3) \(\frac{3}{16}\)
(4) \(\frac{3}{16}\)
Answer:
(3) \(\frac{3}{16}\)

Explaination:
x² + ax + b = 0 ⇒ x = \(\frac{-a \pm \sqrt{a^{2}-4 b}}{2}\)
Given that the roots are real ⇒ a² – 4b ≥ 0 or a² > 4b
When a = 1, b = 1 or 2 or 3 or 4 a² – 4b < 0
When a = 2, b = 1 a² – 4b = 0
When a = 3, b = 1 or 2 for which a² – 4b ≥ 0
When a = 4, b = 1 or 2, 3 or 4 for which a² – 4b ≥ 0
So, Selecting from the 4 number 4² = 16 ways.
(i.e.,) n(s) = 16
n(A) = (2 or 3 or 4) = 3
n(B) = (1 or 2 or 3 or 4) = 4
P(A) + P(B) = \(\frac{3}{16}+\frac{4}{16}=\frac{7}{16}\)

Question 21.
It is given that the events A and B are such that P(A) = \(\frac{1}{4}\), P(A/B) = \(\frac{1}{2}\) and P(B/A) = \(\frac{2}{3}\). Then P(B) is
(1) \(\frac{1}{2}\)
(2) \(\frac{1}{2}\)
(3) \(\frac{1}{2}\)
(4) \(\frac{1}{2}\)
Answer:
(2) \(\frac{1}{2}\)

Explaination:
Given A and B are two events.
Given P(A) = \(\frac{1}{4}\), P(A/B) = \(\frac{1}{2}\)

Question 22.
In a certain college, 4 % of the boys and 1 % of the girls are taller than 1.8 meters. Further 60 % of the students are girls. If a student is selected at random and is taller than 1.8 meters, then the probability that the student is a girl is
(1) \(\frac{2}{11}\)
(2) \(\frac{3}{11}\)
(3) \(\frac{5}{11}\)
(4) \(\frac{7}{11}\)
Answer:
(2) \(\frac{3}{11}\)

Explaination:
Let A₁, A_2, and B be the event of selecting a boy, selecting a girl, and selecting a tall student respectively.

Question 23.
Ten coins are tossed. The probability of getting at least 8 heads is
(1) \(\frac{7}{64}\)
(2) \(\frac{7}{32}\)
(3) \(\frac{7}{16}\)
(4) \(\frac{7}{128}\)
Answer:
(4) \(\frac{7}{128}\)

Explaination:
Favourable events for atleast 8 heads
n(A) = 10C₈ + 10C₉ + 10C₁₀
= 10C₂ + 10C₁ + 10C₀
= \(\frac{10 \times 9}{1 \times 2}\) + 10 + 1
= 5 × 9 + 11 = 45 + 11
n(A) = 56
Ten coins are tossed
∴ n(S) = 2¹⁰ = 1024

Question 24.
The probability of two events A and B are 0.3 and 0.6 respectively. The probability that both A and B occur simultaneously is 0.18. The probability that neither A nor B occurs is
(1) 0.1
(2) 0.72
(3) 0.42
(4) 0.28
Answer:
(4) 0.28

Explaination:
P(A) = 0.3, P(B) = 0.6
P(A ∩ B) = 0.18
So P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
= 0.3 + 0.6 – 0.18
= 0.9 – 0.18 = 0.72
P(A’ ∩ B’) = P[(A ∪ B)’] = 1 – P(A ∪B)
= 1 – 0.72 = 0.28

Question 25.
If m is a number such that m ≤ 5, then the probability that quadratic equation 2x² + 2mx + m + 1 = 0 has real roots is
(1) \(\frac{1}{5}\)
(2) \(\frac{2}{5}\)
(3) \(\frac{3}{5}\)
(4) \(\frac{4}{5}\)
Answer:
(3) \(\frac{3}{5}\)

Explaination:
2x² + 2mx + m + 1 = 0


roots are real ⇒ m² – 2m – 2 ≥ 0
Here m ≤ 5 ⇒ n(S) = 5
When m= 1,m² – 2m – 2
When m = 2, m² – 2m- 2
When m = 3, m² – 2m – 2
When m = 4, m² – 2n- 2
When m = 5, m² – 2m – 2
⇒ n{A) = 3 and so P(A) = \(\frac{3}{5}\)

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 9 Applications of Integration Ex 9.9 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.9

Question 1.
Find by integration, the volume of the solid generated by revolving about the x axis, the region enclosed by y = 2x², y = 0 and x = 1
Solution:
The region to be revolved is sketched

Since revolution is made about the x axis, the volume of the solid generated is given by

Required volume = \(\frac { 4π }{ 5 }\) cubic units

Question 2.
Find, by integration, the volume of the solid generated by revolving about the x axis, the region enclosed by y = e^-2x, y = 0, x = 0 and x = 1.
Solution:
Since revolution is made about the x axis, the volume of the solid generated is given

Required volume = \(\frac { π }{ 4 }\) [1 – e^-4] cubic units

Question 3.
Find, by integration, the volume of the solid generated by revolving about the y axis, the region enclosed by x² = 1 + y and y = 3.
Solution:
The region to be revolved is sketched.

Since revolution is made about the y axis, the volume of the solid generated is given by

Required volume = 8π cubic units

Question 4.
The region enclosed between the graphs of y = x and y = x² is denoted by R. Find the volume generated when R is rotated through 360° about x axis.
Solution:
The region to be revolved is sketched.

Find the intersecting point of y = x and y = x²
x² = x
x² – x = 0
x (x – 1) = 0 x = 0, x = 1
If x = 0, y = 0, x = 1, y = 1
∴ Points of intersection are (0, 0), (1, 1)

Required volume = \(\frac { 2π }{ 15 }\) cubic units

Question 5.
Find, by integration, the volume of the container which is in the shape of a right circular conical frustum as shown to figure.

Solution:
By using integration we have to find the volume of the frustum. So first find the equation of the curve.
Let A(0, 1) and B(2, 2) be two points. Line joining these two points form a straight line. That straight line revolves around x axis.

Volume of the solid revolves around x axis

Volume of the frustum = \(\frac { 14 }{ 3 }\) π m³

Question 6.
A watermelon has an ellipsoid shape which can be obtained by revolving an ellipse with major axis 20 cm and minor axis 10 cm about its major axis. Find its volume using integration.
Solution:
A watermelon has an ellipsoid shape.
2a = 20
a = 10
2b = 10
b = 5

∴ Volume of the frustum = \(\frac { 1000π }{ 3 }\) cubic units.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 9 Applications of Integration Ex 9.8 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.8

Question 1.
Find the area of the region bounded by 3x – 2y + 6 = 0, x = -3, x = 1 and x axis.
Solution:
3x – 2y + 6 = 0
2y = 3x + 6
y = \(\frac { 1 }{ 2 }\)(3x + 6)

Question 2.
Find the area of the region bounded by 2x – y + 1 = 0, y = -1, y = 3 and y axis.
Solution:
Given straight line is 2x – y + 1 = 0
y = 2x + 1, x = \(\frac { y-1 }{ 2 }\)

= 1 + 1
= 2 sq. units
Area required = 2 sq. units

Question 3.
Find the area of the region bounded by the curve 2 + x – x² + y = 0, x axis, x = -3 and x = 3
Solution:
Given curve is
2 + x – x² + y = 0
y = x² – x – 2
y = (x – 2)(x + 1)

Question 4.
Find the area of the region bounded by the line y = 2x + 5 and the parabola y = x² – 2x.
Solution:
First, we find the point of intersection of
y = 2x + 5 and y = x² – 2x
x² – 2x = 2x + 5
x² – 4x – 5 = 0
(x – 5) (x + 1) = 0
x = 5, x = – 1
when x = 5, y = 15
x = -1. y = 3
(5, 15) (-1, 3) are intersecting points.

54 – 18 = 36
Area required = 36 sq. units

Question 5.
Find the area of the region bounded between the curves y = sin x and y = cos x and the lines x = 0 and x = π
Solution:
First find the intersecting point of two curves
sin x = cos x
tan x = 1
x = \(\frac { π }{ 4 }\)

Area required = 2√2 sq. units

Question 6.
Find the area of the region bounded by y = tan x, y = cot x and the lines x = 0, x = \(\frac { π }{ 2}\), y = 0.
Solution:
First find the intersecting point of y = tan x and y = cot x
tan x = cot x
\(\frac { tan x }{ cot x }\) = 1
tan²x = 1
tan x = 1

= log √2 + log √2
= 2 log √2
= log(√2)²
= log 2 sq. units

Question 7.
Find the area of the region bounded by the parabola y² = x and the line y = x – 2.
Solution:
First find the intersecting point of y² = x and y = x – 2
y = y² – 2
y² – y – 2 = 0
y = 2, y = -1
Intersecting points are (4, 2), (1, -1)

Required Area = \(\frac { 9 }{ 2 }\) sq. units

Question 8.
Father of a family wishes to divide his square field bounded by x = 0, x = 4, y = 4 and y = 0 along the curve y² = 4x and x² = 4y into three equal parts for his wife, daughter and son. Is it possible to divide? If so, find the area to be divided among them.
Solution:
Given curve y² = 4x and x² = 4y
Draw these two curves
Also draw the square bounded by the lines
x = 0, x = 4, y = 4 and y = 0
To prove Area A₁ = Area A₂ = Area A₃
Now the point of intersection of the curves y² = 4x and x² = 4y is given by
(\(\frac { y^2 }{ 4 }\))² = 4y
y⁴ = 64y ⇒ y (y³ – 64) = 0
y = 0, y = 4
when y = 0 ⇒ x = 0
y = 4 ⇒ x = 4
Point of intersection are O (0, 0) and B (4, 4)
Now, the area of the region bounded by the curves y² = 4x and x² = 4y is
A₂ = \(\int_{0}^{4}\)(\(\sqrt { 4x }\) – \(\frac { x^2 }{ 4 }\)) dx

Now the area of the region bounded by the curves x² = 4y, x = 4 and x axis is

Similarly the area of the region bounded by the curve y² = 4x, y axis and y = 4 is

Hence we see that
A₁ = A₂ = A₃ = \(\frac { 16 }{ 3 }\) sq. units

Question 9.
The curve y = (x – 2)² + 1 has a minimum point at P. A point Q on the curve is such that the slope of PQ is 2. Find the area bounded by the curve and the chord PQ.
Solution:
Given curve is y = (x – 2)² + 1
(i.e) (y – 1) = (x – 2)²
Vertex of the parabola is (2, 1)
Minimum point P is (2, 1)
Slope of PQ is 2.

Equation of PQ is y – 1 = 2 (x – 2)
y – 1 = 2x – 4
y = 2x – 3
Intersecting point of y = 2x – 3 and y = (x – 2)² + 1
2x – 3 = (x – 2)² + 1
2x – 4 = (x – 2)²
2(x – 2) = (x – 2)²
x – 2 = 2
x = 4
when x = 4, y = 5

Required Area = \(\frac { 4 }{ 3 }\) sq. units

Question 10.
Find the area of the region common to the circle x² + y² = 16 and the parabola y² = 6x
Solution:
First find the intersecting point of the curves
x² + y² = 16 and y² = 6x
x² + 6x = 16
x² + 6x – 16 = 0
(x + 8) (x – 2) = 0
x = -8, x = 2
x = -8 is impossible
x = 2, y = 2√3
Radius of the circle x² + y² = 16 is 4

Area OABC = 2 (Area of OAB)
= 2 (Area of the curve y² = 6x in [0, 2] + Area of the curve x² + y² = 16 in [2, 4])

Required Area = \(\frac { 4 }{ 3 }\) [4π + √3] sq. units

Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 12 Introduction to Probability Theory Ex 12.4 Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 12 Introduction to Probability Theory Ex 12.4

Question 1.
A factory has two Machines – I and II. Machines – I produce 60 % of items and Machine – II produces 40 % of the items of the total output. Further 2 % of the items produced by Machine – I are defective whereas 4 % produced by Machine -II are defective. If an item is drawn at random what is the probability that it is defective?
Answer:
Let A₁ be the event that items are produced by machine – I, A₂ be the event that items are produced by machine – II.
Let B be the event of drawing a defective item. We have to find the total probability of event B. That is P(B) clearly A₁ and A₂ are mutually exclusive and exhaustive events.
∴ P(B) = P(A₁) . P(B/A₁) + P(A₂) . P(B/A₂)

P(B) = P(A₁) . P(B/A₁) + P(A₂) . P(B/A₂)
= 0.60 × 0.02 + 0.40 × 0.04
= 0.012 + 0.016
= 0.028

Question 2.
There are two identical urns containing respectively 6 black and 4 red balls, 2 black, and 2 red balls. An urn is chosen at random and a ball is drawn from it.
(i) Find the probability that the ball is black
(ii) if the ball is black, what is the probability that it is from the first urn?
Answer:

(i) Let A₁ be the event of selecting Urn – I and A₂ be the event of selecting Urn – II.
Let B be the event of selecting one black ball.
We have to find the total probability of event B. That is P(B).
Clearly, A₁ and A₂ are mutually exclusive and exhaustive events.
Probability of selecting Urn – I
P(A₁) = \(\frac{1}{2}\)
Conditional Probability of B, given A₁

Probability of selecting Urn – II
P(A₂) = \(\frac{1}{2}\)
Conditional Probability of B, given A₂

(ii) The conditional Probability of A₁ given B is P(A₁/B)
By Bayes’ theorem

Question 3.
A firm manufactures PVC pipes in the three plants viz, X, Y, and Z. The daily production volumes from the three firms X, Y, and Z are respectively 2000 units, 3000 units, and 5000 units. It is known from past experience that 3 % of the output from plant X, 4 % from plant Y, and 2 % from plant Z are defective. A pipe is selected at random from a day’s total production
(i) find the probability that the selected pipe is a defective one?
(ii) if the selected pipe is defective, then what is the probability that it was produced by plant Y?
Answer:
Let A₁ be the daily volume of production by plant X, A₂ be the daily volume of production by plant Y, A₃ be the daily volume of production by plant Z.
Let B be the defective output we have to find P (B).

(i) Find the probability that the selected pipe is a defective one:
Clearly, A₁, A_2, and A₃ are mutually exclusive and exhaustive events.

Probability that the selected pipe is a defective one = \(\frac{7}{250}\)

(ii) If the selected pipe is defective, then what is the probability that it was produced by plant Y?


Probability that the defective pipe produced by plant Y = \(\frac{3}{7}\)

Question 4.
The chances of A, B, and C becoming manager of a certain company are 5 : 3 : 2. The probabilities that the office canteen will be improved if A, B, and C become managers are 0.4, 0.5 and 0.3 respectively. If the office canteen has been improved, what is the probability that B was appointed as the manager?
Answer:
Let A₁, A_2, and A₃ be the events of A, B, and C becoming managers of the company respectively.
Let B be the event that the office canteen will be improved.
We have to find the conditional probability P (A₂/B).
Since A₁, A₂ and A₃ are mutually exclusive and exhaustive events, applying Bayes theorem.

If the office canteen is improved than the probability of that B was appointed as the manager is \(\frac{15}{41}\)

Question 5.
An advertising executive is studying television viewing habits of married men and women during prime time hours. Based on the past viewing records he has determined that during prime time wives are watching television 60 % of the time. It has also been determined that when the wife is watching television, 40 % of the time the husband is also watching. When the wife is not watching the television, 30 % of the time the husband is watching the television. Find the probability that
(i) the husband is watching the television during the prime time of television
(ii) if the husband is watching the television, the wife is also watching the television.
Answer:

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Accountancy Guide Pdf Chapter 9 Ratio Analysis Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Accountancy Solutions Chapter 9 Ratio Analysis

12th Accountancy Guide Ratio Analysis Text Book Back Questions and Answers

I Multiple Choice Questions

Choose the correct answer

Question 1.
The mathematical expression that provides a measure of the relationship between two figures is called
(a) Conclusion
(b) Ratio
(c) Model
(d) Decision
Answer:
(b) Ratio

Question 2.
Current ratio indicates
(a) Ability to meet short term obligations
(b) Efficiency of management
(c) Profitability
(d) Long term solvency
Answer:
(a) Ability to meet short term obligations

Question 3.
Current assets excluding inventory and prepaid expenses is called
(a) Reserves
(b) Tangible assets
(c) Funds
(d) Quick assets
Answer:
(d) Quick assets

Question 4.
Debt equity ratio is measure of
(a) Short term solvency
(b) Long term solvency
(c) Profitability
(d) Efficiency
Answer:
(b) Long term solvency

Question 5.
Which of the following is not a tool of financial statement analysis?

Answer:
(a) (i) – 1,(ii) – 4,(iii) – 3,(iv) – 2

Question 6.
To test the liquidity of a concern, which of the following ratios are useful?
(i) Quick ratio
(ii) Net Profit ratio
(iii) Debt – equity ratio
(d) Current ratio
Select the correct answer using the codes given below:
(a) (i) and (ii)
(b) (i) and (iv)
(c) (ii) and (iii)
(d) (ii) and iv)
Answer:
(b) (i) and (iv)

Question 7.
Proportion of share holders’ funds to total assets is called
(a) Proprietary ratio
(b) Capital gearing ratio
(c) Debt equity ratio
(d) Current ratio
Answer:
(a) Proprietary ratio

Question 8.
Which one of the following is not correctly matched?
(a) Liquid ratio – Proportion
(b) Gross profit ratio – Percentage
(c) Fixed assets turnover ratio – Percentage
(d) Debt – equity ratio – Proportion
Answer:
(c) Fixed assets turnover ratio – Percentage

Question 9.
Current liabilities ₹ 40,000; Current assets ₹ 1,00,000; Inventory ₹ 20,000. Quick ratio is
(a) 1:1
(b) 2,5:1
(c) 2:1
(d) 1:2
Hint:
Quick ratio or Liquid ratio = \(\frac{\text { Liquid Assets }}{\text { Current liabilities }}\)
Liquid assets = Current Assets – Inventory
= 1,00,000 – 20,000
= 80,000
= \(\frac{80,000}{40,000}\)
= 2:1
= 110%
Answer:
(c) 2:1

Question 10.
Cost of revenue from operation 3,00,000; Inventory at the beginning of the year 60,000; Inventory at the close of the year’ 40,000. Inventory turnover ratio is.
(a) 2 times
(b) 3 times
(c) 6 times
(d) 8 times
Hint:

Answer:
(c) 6 times

II Very Short Answer Questions

Question 1.
What is meant by accounting ratios?
Answer:
The ratio is a mathematical expression of the relationship between two related or interdependent items. It is the numerical or quantitative relationship between two items. It is calculated by dividing one item by the other related item. When ratios are calculated on the basis of accounting information, these are called ‘accounting ratios’.

Question 2.
What is the quick ratio?
Answer:
The quick ratio gives the proportion of quick assets to current liabilities. It indicates whether the business concern is in a position to pay its current liabilities and when they become due, out of its quick assets.

Question 3.
What is meant by debt-equity ratio?
Answer:
It is calculated to assess the long-term solvency position of a business concern. The debt equity ratio expresses the relationship between long term debt and shareholder’s funds.
Debt equity ratio = \(\frac{\text { Long term debt }}{\text { Shareholders funds }}\)
Capital employed = Shareholder’s funds + Noncurrent liabilities
Greater the return on investment better is than the profitability of a business and vice versa.

Question 4.
What does the return on investment ratio indicate?
Answer:
Return on investment shows the proportion of net profit before interest and tax to capital employed (shareholders’ funds and long term debts). This ratio measures how efficiently the capital employed is used in the business. It is an overall measure of the profitability of a business concern.

Question 5.
Statement any two limitations of ratio analysis.
Answer:
Ratios are only means: Ratios are not ended in themselves but they are only means to achieve a particular purpose. Analysis of related items must be done by the management or experts with the help of ratios. Change in price level: Ratio analysis may not reflect price level changes and current values as they are calculated based on historical data given in the financial statement.

III Short Answer Questions

Question 1.
Explain the objectives of ratio analysis.
Answer:
Following are the objectives of ratio analysis:

• To simplify accounting figures
• To facilitate analysis of financial statements
• To analysis the operational efficiency of a business
• To help in budgeting and forecasting
• To facilitate intra firm and inter-firm comparison of performance

Question 2.
What is the inventory conversion period? How is it calculated?
Answer:
The inventory conversion period is the time taken to sell the inventory. A shorter inventory conversion period indicates more efficiency in the management of inventory. It is computed as follows:

Question 3.
How is operating profit ascertained?
Answer:
Operating profit = Revenue from operations – Operating cost
Cost of revenue from operations = Purchases of stock – in – trade + Change in inventories of stock in trade + Direct expenses.
Operating expenses = Administrative expenses + Selling and distribution expenses.
Operating cost = Cost of revenue from operations + Operating expenses.

Question 4.
State any three advantages of ratio analysis.
Answer:
Following are the advantage of ratio analysis:

• Measuring operational efficiency: Ratio analysis helps to know the operational efficiency of a business by finding the relationship between operating cost and revenues and also by comparison of present ratios with those of the past ratios.
• Intra firm comparison: Comparison of the efficiency of different divisions of an organization is possible by comparing the relevant ratios.
• Inter-firm comparison: Ratio analysis helps the firm to compare its performance with other firms.

Question 5.
Bring out the limitations of ratio analysis:
Answer:

• Consistency in preparation of financial statements: Inter firm comparisons with the help of ratio analysis will be meaningful only if the firms follow uniform accounting procedures consistently.
• Non-availability of standards or norms: Ratios will be meaningful only if they are compared with accepted standards or norms. Only few financial ratios have universally recognized standards. For other ratios, comparison with standards is not possible.
• Change in price level: Ratio analysis may not reflect price level changes and current values as they are calculated based on historical data given in financial statements.

IV Exercises

Liquidity ratios

Question 1.
Calculate the current ratio from the following information.

Solution:
Current ratio = \(\frac{\text { Current Assets }}{\text { Current liabilities }}\)
Current Assets = Current Investments + Inventories + Trade Dr’s + B/R+Cash & Cash equivalents
= 40,000 + 2,00,000 + 1,20,000 + 80,000 + 10,000
= Rs. 4,50,000

Current Liabilities
= Trade Cr’s + B/P + Exps. Payable.
= 80,000 + 50,000 + 20,000
= Rs. 1,50,000
Cur. Ratio = \(\frac{4,50,000}{1,50,000}\)
= 3:1
Answer:
Current ratio : 3:1

Question 2.
Calculate quick ratio: Total current liabilities ₹ 2,40,000; total current assets ₹ 4,50,000; Inventories ₹ 70,000; Prepaid Expenses ₹ 20,000
Solution:
Quick Ratio = \(\frac{\text { Quick assets }}{\text { Current liabilities }}\)
Quick assets = Current Assets – Inventories & Prepaid exps.
= 4,50,000 – (70,000 + 2000)
= Rs.3,60,000
Quick Ratio = \(\frac{3,60,000}{2,40,000}\)
=1:5:1
Answer:
Quick ration: 1:5:1

Question 3.
Following is the balance sheet of Lakshmi Ltd. as of 31st March 2019.

Calculate: (i) Current ratio (ii) Quick ratio
Solution:
Current ratio = \(\frac{\text { Current Assets }}{\text { Current liabilities }}\)
Current Assets = Inventories + Trade Dr’s + Cash & Cash equivalents + Prepaid Exps
= 1,60,000 +3,20,000 + 80,000 + 40,000
= Rs. 6,00,000
Current Liabilities = Short term borrowings + Trade Payable + Expenses payable + Short term provisions.
= 50,000 + 3,10,000 + 15,000 + 25,000
= Rs. 4,00,000

Answer:
(i) Current ratio: 1.5:1;
(ii) Quick ratio: 1:1

Question 4.
From the following information calculate debt equity ratio.

Solution:
Debt Equity Ratio = \(\frac{\text { Long term debt }}{\text { Shareholder’s Funds }}\)
Long term debt = Debenture = Rs. 6,00,000
Shareholder’s Fund = Equity share capital + Reserves & Surplus
= 6,00,000 + 2,00,00 = Rs. 8,00,000
Debt Equity Ratio = \(\frac{6,00,000}{8,00,000}\)
= 0.75:1
Answer:
Debt equity ratio: 0.75:1

Question 5.
From the following Balance Sheet of Sundaram Ltd. Calculate proprietary ratio:

Answer:
Proprietary ratio: 0.75:1

Question 6.
From the following information calculate the capital gearing ratio:

Answer:
Capital gearing ratio: 0.5:1

Question 7.
From the following Balance Sheet of James Ltd. as of 31.03.2019 calculate
(i) Debt- Equity ratio
(ii) Proprietary ratio
(iii) Capital gearing ratio

Solution:
Debt Equity Ratio =  \(\frac{\text { Long Term Debt }}{\text { Shareholder’s Fund }}\)|
Shareholder’s Fund
Long term debt = Debentures = Rs. 3,00,000
Shareholder’s Fund = Eq. share capital +Pref. Shares capital + Reserves & surplus
= 2,50,000 ÷ 2,00,000 + 1,50,000
= Rs. 6,00,000

(3) Capital Gearing ratio

= \(\frac{\text { Funds bearing fixed interest (or) Fixed divided }}{\text { Equity shareholder’s Fund }}\)
Funds bearing fixed interest (or) fixed dividend
= Pref. Share Cap + Debentures
= 2,00,000 + 3,00,000 = Rs. 5,00,000
Equity share holder’s Fund .
= Equity Share cap + Reserves & Surplus
= 2,50,000 + 1,50,000
= Rs. 4,00,000
Capital gearing ratio = \(\frac{5,00,000}{4,00,000}\)
= 1.25:1

Answer:

• Debt-equity ration; 0.5:1;
• Proprietary ration; 0.5:1;
• Capital gearing ratio:1.25:1

Question 8.
From the given information calculate the inventory turnover ratio and inventory conversion period (in months) of Devi Ltd.

Solution:
Inventory Turnover Ratio = \(\frac{\text { cost of revenue from operations }}{\text { Average Inventory }}\)
Cost of revenue from operations = Purchase of stock + change in inventories of finished goods operations + Direct Exps.
= Rs. 6,90,000
AverageInventory = \(\frac{\text { Opening Inventory + Closing inventory }}{2}\)
= \(\frac{1,70,000+1,30,000}{2}\)
= Rs. 1,50,000
Change in inventory = Opening inventory – Closing inventory
= 1,70,000 – 1,30,000
= Rs. 40,000
Cost of revenue from operation
= 6,90,000 + 40,000 + 20,000
= Rs. 7,50,000

Answer:
Inventory turnover ratio 5times; Inventory conversion period 2.4 months

Question 9.
The credit revenue from operations of Velavan Ltd, amounted to ₹ 10,00,000. Its debtors and bills receivables at the end of the accounting period amounted to ₹ 1,10,000 and ₹ 1,40,000 respectively. Calculate trade receivables turnover ratio and also.collection period in months.
Solution:
Trade receivable Turnover ratio = \(\frac{\text { Credit revenue from Operations }}{\text { Average trade receivables }}\)
Average trade receivables = \(\frac{\text { Opening trade receivables + Closing trade receivables }}{2}\)
Trade receivable = Trade Drs + B/R
Inventory Turnovers Ratio = \(\frac{10,00,000}{2,50,000}\)
= 4 times
Average Trade receivable
= 1,10,000 + 1,40,000
= Rs. 2,50,000
Debt collection period = \(\frac{\text { Number of months in a year }}{\text { Trade receivable turnover ratio }}\)
= \(\frac{12}{4}\)
= 3 months
Answer:
Trade receivables turnover ratio: 4 time; Debt collection period: 3 months

Question 10.
From the following figures obtained from Arjun Ltd, calculate the trade payable turnover ratio and credit payment period (in days)

Solution:


Answer:
Trade payable turnover ratio: 10 times; Credit payment period: 36.5 days

Question 11.
From the following information of Geetha Ltd., Calculate fixed assets turnover ratio
(i) Revenue from operations during the year was ₹ 55,00,000.
(ii) Fixed assets at the end of the year ₹ 5,00,000
Solution:

Answer:
Fixed assets turnover ratio: 11 times

Question 12.
Calculate

• Inventory turnover ratio
• Trade receivable turnover ratio
• Trade payables turnover ratio and
• Fixed assets turnover ratio from the following obtained from Aruna Ltd.
  

  Particulars	As of 31st March 2018 ₹	As of 31st March 2019 ₹
  Inventory	3,60,000	4,40,000
  Trade receivables	7,40,000	6,60,000
  Trade Payable	1,90,000	2,30,000
  Fixed assets	6,00,000	8,00,000

   

Additional information:

• Revenue from operations for the year ₹ 35,00,000
• Purchases for the year ₹ 21,00,000
• Cost of revenue from operation ₹ 16,00,000
  Assume that sales and purchases are for credit.

Solution




Answer:

• Inventory turnover ratio; 4 times;
• Trade receivable turnover ratio; 5 times;
• Trade payables turnover ratio: 10 times;
• Fixed assets turnover ratio: 5 times

Question 13.
Calculate gross profit ratio form the following: Revenue from operations ₹ 2,50,000, Cost of revenue from operation ₹ 2,10,000 and Purchases ₹ 1,80,000.
Solution:

Answer:
Gross Profit ratio 16%

Question 14.
Following is the statement of profit and loss of Padma Ltd. for the year ended 31st March, 2018. Calculate the operating cost ratio.


Notes to Accounts

Solution:
Operating cost Ratio = \(\frac{\text { Operating cost }}{\text { Revenue from operation }}\) × 100
Operating cost = Cost of revenue from operations + Operating expenses.
Cost of revenue from operations = Purchase + Change in inventory + Direct Expenses
= 8,60,000 + 40,000 + Nil
= Rs. 9,00,000
Operating Exps = Salaries + Office & Administration Exps + Selling+Distribution Exps
= 1,60,000 + 50,000 + 90,000
= Rs. 3,00,000
Operating cost = 9,00,000 + 3,00,000
= Rs, 12,00,000
Operating cost Ratio = \(\frac {12,00000}{15,00000}\) × 100
= 80%
Answer:
Operating cost ratio 80%

Question 15.
Calculate operating profit ratio under the following cases.
Case 1 : Revenue from operations ₹ 8,00,000 Operating Profit ₹ 2,00,000.
Case 2 : Revenue from operations ₹ 20,00,000 Operating Cost ₹ 14,00,000.
Case 3 : Revenue from operations ₹ 10,00,000 Gross profit 25% on revenue from operations, operating expenses ₹ 1,00,000.
Solution:


Answer:
Operating profit ratio – Case 1: 25%; Case 2:30%; Case 3:15%

Question 16.
From the following details of a business, concern calculates net profit ratio.

Solution
Net Profit Ratio = \(\frac{\text { Net Profit }}{\text { Revenue from operations }}\)× 100
Gross profit = Revenue from operations – Cost of revenue from operation
= 9,60,000-5,50,000 Rs. 4,10,000
Operating Profit = Gross Profit – Operating Exps
Operating Exps = Office & Administrative Exps + Selling & Distribution Exps
= 1,45,000 + 25,000 = Rs. 1,70,000
Operating Profit = 4,10,000 – 1,70,000
Operating Profit = Rs. 2,40,000
Net Profit ratio = \(\frac{2,40,000}{9,60,000}\)× 100 = 25%
Answer :
Net Profit ratio 25%

Question 17.
From the following statement of profit. and loss of Dericston Ltd. Calculate
(i) Gross Profit ratio
(ii) Net Profit ratio.

Solution
Gross Profit Ratio = \(\frac{\text { Gross Profit }}{\text { Revenue from operations }}\)×100
Gross profit = Revenue from operations – Cost of revenue from operation
Cost of revenue from operations = Purchase + Change in inventories
= 18,80,000 – 80,000 = Rs. 18,00,000
Gross Profit = 24,00,000 – 18,00, 000 = Rs. 6,00,000

Answer :

• Gross profit ratio of 25%
• net Profit ratio 10%

Question 18.
From the following trading activities of Jones Ltd. Calculate

• Gross profit ratio
• Net Profit ratio
• Operating cost ratio
• Operating profit ratio

Solution
(1) Gross Profit Ratio = \(\frac{\text { Gross Profit }}{\text { Revenue from operations }}\)× 100
cost of Revenue from operations = Purchase + Change in inventories
= 2,10,000 + 30,000
= Rs. 2,40,000
Gross profit = Revenue from operations – cost of revenue from operations
= 4,00,000 – 2,40,000
= Rs. 1,60,000
Gross Profit ratio = \(\frac{1,60,000}{4,00,000}\)× 100 = 40%


Answer :

• Gross profit ratio 40%
• Net Profit ratio 20%
• Operating cost ratio 75%
• Operating profit ratio 25%

Question 19.
Following is the extract of the balance sheet of Abdul Ltd., as of 31st March 2019

Net Profit before interest and tax for the year was ₹ 60,000. Calculate the return on capital employed for the year.
Solution:

Answer :
Return on capital employed: 15%

12th Accountancy Guide Ratio Analysis Additional Important Questions and Answers

Other Important question & Answers
Question 1.
All solvency ratios are express in terms of
(a) Proportion
(b) Times
(c) Percentage
Answer:
(b) Times

Question 2.
All activity ratios, (or) Turnover ratios in terms of
(a) Proportion
(b) Times
(c) Percentage
Answer:
(b) Times

Question 3.
All profitability ratios are expressed in terms of ………………
(a) Proportion
(b) Times
(c) Percentage
Answer:
(c) Percentage

Question 4.
Shareholders funds include
(a) Equity share capital, preference share capital reserves & Surplus
(b) Loans from banks & financial institutions.
(c) Equity share capital, preference share capital, reserves & surplus, and loans from banks & financial institutions.
Answer:
(a) Equity share capital, preference share capital reserves & Surplus

Question 5.
The current ratio is a
(a) Solvency ratio
(b) Profitability ratio
(c) Liquidity ratio
Answer:
(a) Solvency ratio

Question 6.
The ratio is expressed in ……………… way
(a) 2
(b) 4
(c) 3
Answer:
(c) 3

Question 7.
The cost of revenue from the operation is Rs. 4,00,000. Average inventories Rs. 8,00,000 Inventory turnover ratio is
(a) 5 times
(b) 4 times
(c) 7 times
Answer:
(a) 5 times

Question 8.
The operating ratio is equal to
(a) 100-operating profit ratio
(b) 100 +operating profit ratio
(c) Operating profit ratio
Answer:
(a) 100-operating profit ratio

Question 9.
Operating expenses include
(a) Selling & administration expenses
(b) Selling & administration expens
(c) a & b
Answer:
(c) a & b

Question 10.
Equity share capital Rs. 2,00,000 Reserves & Surplus Rs. 30,000 Debenture Rs. 40,000 and shareholders fund will be.
(a) Rs. 200,000
(b) 2,70,000
(c) Rs. 2,30,000
Hint:
Share holder fund = Equity share capital + Reserve and surplus
= 2,00,000 + 30,000
= ₹ 2,30,000
Answer:
(c) Rs. 2,30,000

III Short Answer Questions

Question 1.
Define Ratio Analysis
Answer:
According to Myers, “Ratio analysis is a study of the relationship among various financial factors in a business”.

Question 2.
What do you mean by ratio Analysis?
Answer:
Ratio analysis is a tool which involves analyzing the financial statements by calculating various. It is a tool of financial statement analysis, in which, inferences are drawn based on the computation and analysis of different ratios.

Question 3.
What are the two ways of classifying the ratios?
Answer:
Ratios may be classified in the following two ways:

• Traditional classification
• Functional classification

Question 4.
What do you mean by the traditional classification of ratio? Explain
Answer:
The traditional classification of ratios is done on the basis of the financial statements from which the ratios are calculated. Under the traditional classification, the ratio is classified as:

• Balance sheet ratio: If both items in a ratio are from the balance sheet, it is classified as a balance sheet ratio.
• Income statement ratio: If the two items in a ratio are from the income statement, it is classified as an income statement ratio.
• Inter – Statements ratio: If a ratio is computed with a tone item from the income statement and another item from the balance sheet, it is called an inter-statement ratio.

Question 5.
What is the functional classification of ratios?
Answer:
Under the functional classification, the rations are classified as follows:

• Liquidity ratios
• Long term solvency ratios
• Turnover ratios.
• Profitability ratios.

Question 6.
What do you mean by Liquidity ratios?
Answer:
Liquidity means the capability of being converted into cash with ease. Liquidity ratios help to assess the ability of a business concern to meet its short term financial obligations. Short term assets (current assets) are more liquid as compared to long term assets (fixed assets). Liquidity ratios are also called as short term solvency ratios.

Question 7.
What do you mean by the current ratio?
Answer:
Current ratio gives the proportion of current assets to current liabilities of a business concern. It is computed by dividing current assets by current liabilities. The current ratio indicates the ability of an entity to meet its current liabilities as and when they are due for payment.

Question 8.
What do you mean by Long-term solves ratios? what are its types?
Answer:
Long term solvency means the firm’s ability to meet its liabilities in the long run. Long term solvency ratios help to determine the ability of the business to repay its debts in the long run. The following ratios are normally computed for evaluating long term solvency of the business:

• Debt equity ratio
• proprietary ratio
• Capital gearing ratio

Question 9.
What do you mean by Turnover Ratios? What are its types?
Answer:
Turnover ratios show how efficiently assets or other items have been used to generate revenue from operations. They are also called as activity ratios or efficiency ratios. They how the speed of movement of various items. They are expressed as number of times in relation to the item compared.
The important turnover ratios are:

• Inventory turnover ratio
• Trade receivable turnover ratio
• Trade payable turnover ratio
• Fixed assets turnover ratio.

Question 10.
What do you mean by Trade Receivable Turnover ratio?
Answer:
Trade receivable turnover ratio is the comparison of credit revenue from operations with average trade receivables during an accounting period. It gives the velocity of the collection of cash from trade receivables.

Question 11.
What do you mean by Debt collection Period?
Answer:
Debt collection period is the average time taken to collect the amount due from trade receivables. Lesser the debt collection period, grater is the efficiency of management in the collection of cash from trade receivables. It is calculated as follows.

What do you mean by Trade payable Turnover ratio?
Trade payable turnover ratio is the comparison of net credit purchases with average trade payables during an accounting period. It gives the velocity to payment of cash towards trade payables.

Question 12.
What do you mean by credit payment period?
Answer:
It is the average time taken by the business for payment of accounts payable. Lesser the credit payment period, greater is the efficiency of the management in managing accounts payable as it indicated quicker settlement of trade payables. It is calculated as follows:

Question 13.
What do you mean by Fixed Assets Turnover
Answer:
The fixed assets turnover ratio gives the number of times the fixed assets are turned over during the year in relation to the revenue from operations. This ratio indicates the efficiency of utilization of fixed assets.

Question 14.
What do you mean by profitability ratios? What are its types?
Answer:
Profitability ratios help to assess the profitability of a business concern. These rations also help to analyze the earning capacity of the business in terms of utilization of resources employed in the business. Generally, these rations are expressed as a percentage.
The profitability ratios commonly used are:

1. Gross profit ratio
2. Operating cost ratio
3. Operating profit ratio
4. Net profit ratio
5. Return on investment.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Accountancy Guide Pdf Chapter 5 Admission of a Partner Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Accountancy Solutions Chapter 5 Admission of a Partner

12th Accountancy Guide Admission of a Partner Text Book Back Questions and Answers

I. Multiple Choice Questions

Choose the correct answer

Question 1.
Revaluation A/c is a
(a) Real A/c
(b) Nominal A/c
(c) Personal A/c
(d) Impersonal A/c
Answer:
(b) Nominal A/c

Question 2.
On revluation, the increase in the value of assets leads to
(a) Gain
(b) Loss
(c) Expense
(d) None of these
Answer:
(a) Gain

Question 3.
The profit or loss on revaluation of assets and liabilities is transferred to the capital account of
(a) The old partners
(b) The new partner
(c) All the partners
(d) The Sacrificing partners
Answer:
(a) The old partners

Question 4.
If the old profit sharing ratio is more than the new profit sharing ratio of a partner, the difference is called
(a) Capital ratio
(b) Sacrificing ratio
(a) all the partners
(b) the old partners
(c) the new partner
(d) the sacrificing partners
Answer:
(b) Sacrificing ratio

Question 6.
Which of the following statements is not true in relation to the admission of a partner
(a) Generally mutual rights of the partners change
(b) The profits and losses of the previous years are distributed to the old partners
(c) The firm is reconstituted under a new agreement
(d) The existing agreement does not come to an end
Answer:
(d) The existing agreement does not come to an end

Question 7.
Match List-I with List-II and select the correct answer using the codes given below:

Answer:
b

Question 8.
Select the odd one out
(a) Revaluation profit
(b) Accumulated loss
(c) Goodwill brought by a new partner
(d) Investment fluctuation fund
Answer:
(c) Goodwill brought by a new partner

Question 9.
James and Kamalesh are partners sharing profits and losses in the ratio of 2:1. They admit Yogesh into partnership. The new profit sharing ratio between Balaji, Kamalesh, and Yogesh is agreed to 3:1:1. Find the sacrificing ratio.
(a) 1:3
(b) 3:1
(c) 5:3
(d) 3:5
Hint:

Answer:
(c) 5:3

Question 10.
Balaji and Kamalesh are partners sharing profits and losses in the ratio of 2:1. They admit Yogesh into partnership. The new profit sharing ratio between Balaji, Kamalesh and Yogesh is agreed to 3:1:1. Find the sacrificing ratio between Balaji and Kamalesh.
(a) 1:3
(b) 3:1
(c) 2:1
(d) 1:2
Hint:
Sacrifice ratio = old ratio – new ratio
Old partner’s = Balaji, Kamalesh

Answer:
(d) 1:2

II. Very Short Answer Questions

Question 1.
What is meant by the revaluation of assets and liabilities?
Answer:
When a partner is admitted into the partnership the assets and liabilities are revealed as the current value may differ from the book value. Determination of current values of assets and liabilities is called revaluation of assets and liabilities.

Question 2.
How are accumulated profits and losses distributed among the partner at the time of admission of a new partner?
Answer:
The following and the adjustment are necessary at the time of admission of a partner.

•  Distribution of accumulated profits, reserves, and losses
•  Revaluation of assets and liabilities
•  Determination of new profit – sharing ratio and sacrificing ratio
•  Adjustment for goodwill
•  Adjustment of capital on the basis of the new profit sharing ratio (if no agreed).

Question 3.
What is sacrificing ratio?
Answer:
The sacrificing ratio is the proportion of the profit which is sacrificed or foregone by the old partners in favour of the new partner. The purpose of finding the sacrificing ratio is to share the goodwill brought in by the new partner.
Sacrifice Ratio = Old share – New share

Question 4.
Give the journal entry for writing off existing goodwill at the time of admission of a new partner.
Answer:
Old partners capital /current A/c (in old ratio) Dr. To G/W A/c

Question 5.
State whether the following will be debited or credited in the revaluation account.
Answer:

1. Depreciation on assets – Debited
2. Unrecorded liability – Debited
3. Provision for outstanding expenses – Debited
4. Appreciation of assets – Credited

III Short Answer Questions

Question 1.
What are the adjustments required at the time of admission of a partner?
Answer:
The following adjustments are necessary at the time of admission of a partner.

1. Distribution of accumulated profits, reserves, and losses
2. Revaluation of assets and liabilities
3. Determination of new profit sharing ratio and sacrificing ratio
4. Adjustment for goodwill
5. Adjustment of capital on the basis of new profit sharing ratio

Question 6.
What are the journal entries to be passed on revaluation of ssets and liabilities?
Answer:
Following are the journal entries to be passed to record the revaluation of assets and liabilities:

Question 7.
Write a short note on the accounting treatment of goodwill.
Answer:
Accounting treatment for goodwill on the admission of a partner is discussed below:

Question 1.
When a new partner brings cash towards goodwill
Answer:
When the new brings cash towards goodwill in addition to the amount of capital, it is distributed to the existing partners in the sacrificing ratio.
If the new partner does not bring goodwill in cash or in kind, his share of goodwill must be adjusted through the capital accounts of the partners.

Sometimes the new partner may bring only a part of the goodwill in cash or assets. In such a case, for the cash or the assets brought, the respective account is debited and for the amount not brought in cash or kind, the new partner’s capital account is debited.

If goodwill already appears in the books of accounts, at the time of admission if the partners decide, it can be written off by transferring it to the existing partner s capital account / current account in the old profit sharing ratio.

IV Exercises

Distribution of accumulated profits, reserves, and losses

Question 1.
Arul and Anitha are partners sharing profits and losses in the ratio of 4:3. On 31.03.2018, Ajay was admitted as partner. On the date of admissions, the book of the firm showed a general reserve of ₹ 42,000. Pass the journal entry to distribute the general reserve.
Solution:

(General reserve transferred to old partners capital A/c in the old profit sharing ratio 4:3.)
Answer :
Arul: ₹ 24,000 (Cr.); Anitha: ₹ 18,000 (Cr.)

Question 2.
Anjali and Nithya are partners of firms sharing profits and losses in the ratio of 5:3. They admit Pramila on 01.01.2018. On that date, their balance sheet showed an accumulated loss of ₹ 40,000 on the asset side of the balance sheet. Give the journal entry to transfer the accumulated loss on admission.
Solution:

(Accumulated loss transferred to old partner s capital A/cs in the old ratio.)
Answer:
Profit and loss: ₹ 25,000 (Dr.); Nithya: ₹ 15,000(Dr.)

Question 3.
Oviya and Kavya are partners in firm sharing profits and losses in the ratio of 5:3. They admit Agalya into the partnership. Their balance sheet as of 31st March 2019 is as follows:

The pass journal entry to transfer the accumulated profit and reserve on admission.
Solution:

Accumulated profits and reserve transferred to old partners capital A/c in the old ratio
Answer :
Oviya : ₹ 37,500; Kavya : ₹ 22,500

Question 4.
Hari, Madhavan, and Kesavan are partners, sharing profit and losses in the ratio of 5:32. As from 1st April 2017, Vanmathi is admitted into the partnership and the new profit sharing ratio is decided as 4:3:2:1. The folio 5 adjustments are to be made.
(a) Increase the value of premises by ₹ 60,000.
(b) Depreciate stock by ₹ 5,000, furniture by ₹ 2, 000 and machinery by ₹ 2,500.
(c) Provide for an outstanding liability of ₹ 500.
Pass journal entries and prepare revaluation account.
Solution:

Question 5.
Seenu and Siva are partners sharing profits and losses in the ratio of 5:3. In view of kowsalya admission, they decided.
(i) To increase the value of the building by ₹ 40,000.
(ii) To bring into record investment at ₹ 10,000, Which have not so far been brought into
(iii) To decrease the value of machinery by ₹ 14,000 and furniture by ₹ 12,000.
(iv) To write off sundry creditors by ₹ 16,000.
Pass journal entries and prepare revaluation account
Solution :

Answer:
Revolution Profit in Rs. 40.000

Question 6.
Sai and Shankar are partners, sharing profits and losses in the ratio of 5:3.The firm’s balance sheet as on 31st December, 2017, was as follows:


On 31st December 2017, Shanmugam was admitted into the partnership for 1/4 share of profit with ₹ 12,000 as capital subject to the following adjustments.
(a) Furniture is to be revalued at ₹ 5,000 and the building is to be revalued at ₹ 50,000.
(b) Provision for doubtful debts is to be increased to ₹ 5,500
(c) An unrecorded investment of ₹ 6,000 is to be brought into account.
(d) An unrecorded liability of ₹ 2,500 has to be recorded now.
Pass journal entries and prepare Revaluation Account and capital account of partners after admission.
Solution:


Answer:
Revaluation Profit: ₹16,000; Capital accounts; Sai: ₹ 58,000 (Cr.), Shankar: ₹ 46,000 (Cr.); Shanmugam: ₹ 12,000 (Cr.))

Question 7.
Amal and Vimal are partners in firm sharing profits and losses in the ratio of 7:5. Their valance sheet as of 31st March 2019, is as follows:

Nirmal is admitted as a new partner on 01.04.2018 by introducing a capital of 30,000 for 1/3 share in the future profit subject to the following adjustments.
(a) Stock to be depreciated by ₹ 5,000;
(b) Provision for doubtful debts to be created for ₹ 3,000
(c) Land to be appreciated by ₹ 20,000.
Prepare revaluation account and capital account of partners after admission.
Solution:

Answer:
Revaluation Profit: ₹ 12,000; Capital accounts: Amal ₹ 91,000 (Cr.), Vimal ₹ 65,000 (Cr.), Nirmal ₹ 30,000 (Cr.))

Question 8.
Praveena and Dhanya are partners sharing profits in the ration of 7:3 they admit Malini into the firm. The new ratio among Praveena, Dhanya, and Malini are 5:2:3. Calculate the sacrificing ratio.
Solution:
Sacrificing ratio = Old share – New share
OR = 7:3 NR = 5:2:3
Praveena
SR = OR – NR
\(\frac{7}{10}-\frac{5}{10}=\frac{2}{10}\)
Dhanya
= \(\frac{3}{10}-\frac{2}{10}=\frac{1}{10}\)
SR = OR – NR
SR = 2:1
Answer :
Sacrificing ratio = 2:1

Question 9.
Ananth and Suman are partners sharing profits and losses in the ratio of 3:2. They admit Saran for 1/5 share, which he acquires entirely from Ananth. Find out the new profit sharing ratio and sacrificing ratio.
Solution :

Answer:
New profit sharing ratio: 2:2:1 Sacrificing ratio 1:0

Question 10.
Raja and Ravi are partners, sharing profit in the ratio of 3:2. They admit Ram for 1/4 share of the Profit, he takes 1/20 share from Raja and 4/20 from Ravi. Calculate the new profit sharing ratio and sacrificing ratio.
Solution:


Answer :
New Profit sharing ratio: 11:4:5; Sacrificing ratio 1: 4

Question 11.
Vimala and Kamala are partners, sharing profits in the ratio of 4:3. Vinitha enters into the partnership and she acquires 1/14 from Vimala and 1/14 from Kamala. find out the new profit sharing ratio and sacrificing ratio.
Solution:

Answer :
New Profit sharing ratio 7 : 5 : 2; sacrificing ratio 1 : 1

Question 12
Govinda and Gopal are partners is a firm sharing profit^ in the ratio of 5 : 4. They admit Rahim as a partner. Govind surrenders 2/9 of his share in favour of Rahim. Gopal surrenders 1 /9 of his share in favour of R thim. Calculate the new profit sharing ratio and sacrificing ratio.
Solution:


Answer:
New profit sharing ratio 35:32:14; Sacrificing ratio 5:2

Question 13.
Prema and Chandra share profits in the ratio of 5:3. Hema has admitted a partner. Prema surrendered 1 /8 of her share and Chandra surrendered 1 /8 of her share in favour of Hema. Calculate the new profit sharing ratio and sacrificing ratio.
Solution:
Prema : Chandra → 5:3 (OR)
Sacrificing Ratio

Answer:
New profit sharing ratio 35:21:8; Sacrificing ratio 5:3

Question 14.
Karthik and Kannan are equal partners. They admit Kailash with 1/4 share of the profit. Kailash acquired his share from old partners in the ratio of 7:3 Calculate the new profit sharing ratio and sacrificing ratio.
Solution :
Sacrificing Ratio → Share of New Parter 1/4 → Sacrificed → 7 : 3
karthicks SR

Answer:
New profit sharing ratio 13:17:10; Sacrificing ratio 7:3

Question 15.
Selvam and Senthil are partners sharing profit in the ratio of 2:3. Siva is admitted into the firm with 1/5 share of profit. Siva acquires equally from Selvam and Senthil. Calculate the new profit sharing ratio and sacrificing ratio.
Solution:

Answer:
New profit sharing ratio 3:5:2; Sacrificing ratio 1:1

Question 16.
Mala and Anitha are partners, sharing profits and losses in the ratio of 3:2. Mercy is admitted into the partnership with 1/5 share in the profits. Calculate new profit sharing ratio and sacrificing ratio.
Solution:
Since share sacrificed proportion and new profit sharing ratio are not given, it is assumed that the existing partners sacrifice in their old profit sharing ratio that is 3:2
Sacrificing Ratio

Answer:
New profit sharing ratio 12:8:5; Sacrificing ratio 3:2

Question 17.
Ambika, Dharani and Padma are partners in a firm sharing profile in the ratio of 5:3:2. they admit Ramya for 25% profit. Calculate the new profit sharing ratio and sacrificing ratio.
Solution:

Answer:
New profit sharing ratio 15:9:6:10; Sacrificing ratio 5:3:2

Adjustment for goodwill

Question 18.
Aparna and Priya are partners who share profits and losses in the ratio of 3:2. Brindha joins the firm for 1/5 share of profits and brings in cash for her share of the goodwill of Rs. 10,000. Pass necessary journal entry for adjusting goodwill on the assumption that the fluctuating capital method is followed and the partners withdraw the entire amount of their share of goodwill.
Solution:


Answer:
Share of goodwill: Aparna: ₹ 6,000; Priya ₹ 4,000

Question 19.
Deepak, Senthil, and Santhosh are partners sharing profits and losses equally. They admit Jerald into a partnership for 1/3 share in future profits. The goodwill of the firm is valued at ₹ 45,000 and Jerald brought cash for his share of goodwill. The existing partners withdraw half of the amount of their share of goodwill. Pass necessary journal entries for adjusting goodwill on the assumption that the fluctuating capital method is followed.
Solution:
Jerald’s share of G/w = 45,000 x \(\frac{1}{3}\) = Rs. 15,000

Answer:
Share of goodwill: Deepak: ₹ 5,000; Senthil: ₹ 5,000; Santhosh: ₹ 5,000

Question 20.
Malathi and Shobana are partners sharing profits and losses in the ratio of 5:4. They admit Jayasri into a partnership for 1/3 share of profit. Jayasri pays cash ₹ 6,000 towards her share of goodwill. The new ratio is 3:2:1. Pass necessary journal entry for adjusting goodwill on the assumption that the fixed capital method is followed.
Solution:
= OR – NR
OR = 5:4
New Ratio = 3:2:1

Answer:
Share of goodwill: Malathi’s Current account: ₹ 2,000; Shobana’s Current account: ₹ 4,000;

Question 21.
Anu and Arul were partners in a firm sharing profits and losses in the ratio of 4:1. They have decided to admit Mano into the firm for 2/5 share of profits. The goodwill of the firm on the date f admission was valued at ₹ 25,000. Mano is not able to bring in cash for his share of goodwill. Pass necessary journal entry for goodwill on the assumption that the fluctuating Capital method is followed.
Solution:
Mano’s Share of G/w = 25,000 x 2/5 = Rs. 10,000

Answer:
Share of goodwill: Anu: ₹ 8,000; Arul: ₹ 2,000;

Question 22.
Varun and Barath are sharing profits and losses 5:4. They admit Dhamu into partnership. The new profit sharing ratio is agreed at 1:1:1. Dhamu’s share of goodwill is valued at ₹ 15,000 of which he pays ₹ 10,000 in cash. Pass necessary journal entries for adjustment of goodwill on the assumption that the fluctuating capital method is . followed. ‘
Answer:

Answer:
Share of goodwill: Varun : ₹ 10,000; Barath : ₹ 5,000;

Question 23.
Sam and Jose are partners in the firm sharing profits and losses in the ratio of 3:2. On 1st April 2018, they admitted Joel as a partner. On the date of Joel’s admission, goodwill appeared in the books of the firm at ₹ 30,000. By assuming the fluctuating capital method, pass the necessary journal entry if the partners decide
(a) Write off the entire amount of existing goodwill
(b) write off ₹ 20,000 of the existing goodwill.
Solution :
To write off the entire amount of goodwill

Answer:
Share of goodwill: (a) Sam: ₹ 18,000 (Dr); Jose : ₹ 12,000 (Dr) (b) Sam: ₹ 12,000 (Dr); Jose: ₹ 8,000 (Dr.))

Comprehensive problems:

Question 24.
Rajan and Selva are partners sharing profits and losses in the ratio of 3:1. Their balance sheet as on 31st March 2017 is as under.

On 01.04.2017, they admit Ganesan as a new partner on the following arrangements.
(i) Ganesan brings ₹ 10,000 as capital for 1/5 share of profit.
(ii) Stock and furniture are to be reduced by 10%, a reserve of 5% on debtors for doubtful debts is to be created.
(iii) Appreciate buildings by 20%
Prepare revaluation account, partner’s capital account, and the balance sheet of the firm after admission.
Solution :


Answer:
Revaluation profit:: ₹ 2,100; Capital accounts : Rajan : 27075; Selva; ₹ 15,025; Ganesan : ₹ 10,000 Balance sheet total: ₹ 89,600

Question 25.
Sundar and Suresh are partners sharing profit in the ratio of 3 : 2. Their balance sheet as on 1st January 2017 was as follows:

They decided to admit Sugumar into a partnership for 1/4 share in the profits on the following terms:
(a) Sugumar has to bring in ₹ 30,000 as capital. His share of goodwill is valued at Rs. 5,000. He could not bring cash towards goodwill.
(b) That the stock is valued at ₹ 20,000.
(c) That the furniture is depreciated by ₹ 2,000.
(d) That the value of building be depreciated by 20%
Prepare necessary ledger accounts and the balance sheet after admission.
Solution:



Answer:
Answer:
Revaluation loss : ₹ 15,000; Capital accounts: Sundar : ₹ 39,000; Suresh; ₹ 26,000; Sugumar : ₹ 25,000 Balance sheet total ₹ 1,40,000

Question 26.
The following is the balance sheet of James and Justina as on 1.1.2017. They share the profits and losses equally.

On the above date, Balan is admitted as a partner with a 1/5 share in future profits. Following are the terms for his admission:
(i) Balan brings ₹ 25,000 as capital.
(ii) His share of goodwill is ₹ 10,000 and he brings cash for it.
(iii) The assets are to be valued as under:
Building ₹ 80,000; Debtors ₹ 18,000; Stock ₹ 33,000
Prepare necessary ledger accounts and the balance sheet after admission.
Solution:


Answer:
Revaluation profit:: ₹ 11,000; Capital accounts : James : ₹ 58,000; Justina; ₹ 68,000; Balan : ₹ 25,000 Balance sheet total: ₹ 1,86,000

Question 27.
Anbu and Shankar are partners in a business sharing profits and losses in the ratio of 7:5. The balance sheet of the partners on 31.03.2018 is as follows:

Rajesh is admitted for 1/5 share on the following terms:
(i) Goodwill of the firm is valued at ₹ 80,000 and Rajesh brought cash ₹ 6,000 for his share of goodwill.
(ii) Rajesh is brought ₹ 1,50,000 as his capital.
(iii) Motor car is valued at ₹ 2,00,000; stock at ₹ 3,80,000 and debtors at ₹ 3,50,000.
(iv) Anticipated claim on workmen compensation fund is ^ 10,000
(v) Unrecorded investment of ₹ 5,000 has to be brought into account.
Prepare revaluation account, capital account, and balance sheet after Rajesh’s admission.
Solution:


Answer:
Revaluation profit:: ₹ 15,000; Capital accounts: Anbu: ₹ 5,11,417; Shankar; ₹ 3,79,583; Rajesh : ₹ 1,50,000 Balance sheet total: ₹ 11,71,000

12th Accountancy Guide Admission of a Partner Additional Important Questions and Answers

Question 1.
When A and B sharing profit and losses in the ratio of 3:2. They admit C as a partner giving him 1 /3 share of profits. This will be given by A 8t B
(a) Equally
(b) in the ration of their
(c) in the ratio of profits
Answer:
(c) in the ratio of profits

Question 2.
In order to maintain fair dealings at the time of admission, it is necessary to revalue assets 8t liabilities of the firm to their
(a) Cost Price
(b) Cost price less depreciation
(c) True value.
Answer:
(c) True value.

Question 3.
If the new share of the incoming partner is given without mentioning the details of the sacrifice made by the old partners then the presumption is that old partners sacrifice in the
(a) Old profit sharing ration
(b) Gaining ratio
(c) Capital ratio.
Answer:
(a) Old profit sharing ration

Question 4.
On admission of a new partner, the balance of general Reserve A/c should be transferred to the capital account of
(a) all partners in their new profit sharing ratio
(b) Old partners in their new old profit sharing ratio
(c) Old partners in their new profit sharing ratio.
Answer:
(b) Old partners in their new old profit sharing ratio

Question 5.
The old partners share all the accumulated profit & reserves in their
(a) new profit sharing ratio
(b) Old profit sharing ratio
(c) Capital ratio
Answer:
(b) Old profit sharing ratio

Question 6.
Hie reconstitution of the partnership requires a revision of the existing partners
(a) Profit sharing ratio
(b) Capital ratio
(c) Sacrificing ratio|
Answer:
(a) Profit sharing ratio

Question 7.
……………… ratio is computed at the time by the admission of a partner
(a) gaining ratio
(b) Capitalization
(c) Sacrificing ratio
Answer:
(c) Sacrificing ratio

Question 8.
When unrecorded liability is brought in to books of accounts, it results in
(a) profit
(b) loss
(c) Neither profit nor loss
Answer:
(b) loss

IV Additional Problems:

Question 1.
Anandan and Balaraman partners in a firm with a capital of Rs. 70,000 and Rs. 50,000 respectively. They decided to admit Chandran into the firm with a capital of Rs. 40,000. Give journal entry for Capital brought in by Chandran.
Solution :

Question 2.
Rathai and Kothai are partners sharing profits in the ratio of 3:2. They admit Kanmani for 1/5th share of future profits which she acquires 3/20th from Rathai and 1/20th from Kothai. Calculate new Pro iring ratio and. sacrifice s ratio of old partners.
Solution :

Question 3.
P and Q are partners sharing profits in the ratio of 3:2. They admit R for 1/5th Share which acquires equally from P and Q. Calculate new profit sharing ratio and sacrificing ratio of old partners.
Solution:

Question 4.
Sankar and Saleem are partner in a firm sharing profits and losses in the ration of 3:2 as on 31st March 2005. Their Balarr sheet was as under.

On 1st April 2005, they admit Solomon into partnership on the following condition: Solomon has brought Rs. 1,00,000 as capital.
The value of land and building was to be increased by Rs. 20,000.
Stock and furniture were to be depreciated by Rs. 10,000 and Rs. 5,000 respectively. Rs. 15,000 to be written off from sundry creditors as it is no longer liable.
Provision for doubtful debts is to be increased by Rs. 1,000.
Give journal entries, prepare Revaluation Account and the Balance Sheet.
Solution:

Question 5.
Amar and Akbar are partners in a firm sharing profits and losses in the ratio of 2:1  as 31st March 2005. Their Balan Sh» was as under.

On 1st April 2005, they admit Antony into partnership on the following conditions:
Antony has brought in the capital of Rs. 1,50,000 for 1/5th share of the future profits. Stock and machinery were to be depreciated by Rs. 6,000 and Rs. 15,000 respectively.
Investments Rs. 15,000 not recorded in the books brought into accounts.
Provision for doubtful debts is to be created at 5% on debtors.
A liability of Rs. 4,000 for outstanding repairs has been omitted to be recorded in the books. Give journal entries, prepare Revaluation Account, Capital Account, Bank Account, and the Balance Sheet.
Solution:

Question 6.
Sumathi and Sundari are partners of a firm sharing profit and loss in the ratio of 4 :3. Their Balance Sheet shows Rs. 14,000 as Profit and Loss A/c on the liabilities side. Pass entry.
Solution:

Question 7.
Mahalakshmi and Dhanalakshmi are partners sharing profit and loss in the ratio of 3:2. They admit Deepalakshmi on 1st January 2005. On that date, their Balance Sheet showed an amount of Rs. 25,000 as Profit and Loss A/c in the Asset side. Pass entry.
Solution:

Question 8.
Damodaran and Jagadeesan are partners sharing profits in the ratio of 3:2. They decided to admit Vijayan for 1/5th share of future profit. Goodwill of the firm is to be valued at Rs. 50,000.
Give Journal entries, if
There is no goodwill in the books of the firm.
The goodwill appears at Rs. 30,000
The goodwill appears at Rs. 60,000.
Solution:

Question 9.
Sankari and Sudha are partners sharing profit and loss in the ratio of 3:2. Their Balance Sheet as on 31st March 2005 is as under.

They decided to admit Santhi into the partnership with effect from 1st April 2005 on the following terms:
Santhi to bring in Rs. 60,000 as Capital for 1/3rd share of profits.
Goodwill was valued at Rs. 45,000
The land was valued at Rs. 1,50,000
The stock was to be written down by Rs. 8,000
The provision for doubtful debts was to be increased to Rs. 3,000
Creditors include Rs. 5,000 no longer payable and this sum was to be written off.
Investment of Rs. 10,000 be brought into books.
Prepare Revaluation A/c, Capital A/c, and Balance Sheet of the new firm.
Solution :

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 9 Applications of Integration Ex 9.7 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.7

Question 1.
Evaluate the following
(i) \(\int_{0}^{∞}\) x⁵ e^-3x dx
Solution:

(ii) \(\int_{0}^{π/2}\) \(\frac{e^{-tanx}}{cos^6 x}\) dx
Solution:

Question 2.
\(\int_{0}^{∞}\) sin^αx² x³ dx = 32, α > 0, find α
Solution: