Tamilnadu State Board New Syllabus Samacheer Kalvi 8th Maths Guide Pdf Chapter 4 Life Mathematics Ex 4.4 Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 4 Life Mathematics Ex 4.2

Question 1.

Fill in the blanks:

(i) Loss or gain percentage is always calculated on the ________ .

Answer:

Cost Price

(ii) A mobile phone is sold for ₹ 8400 at a gain of 20%. The cost price of the mobile phone is ________ .

Answer:

₹ 7000

Hint:

Let cost price of mobile be ₹ x

Given that selling price is ₹ 8400 and gain is 20%

As per formula,

(iii) An article is sold for ₹ 555 at a loss of 7\(\frac { 1 }{ 2 }\)%. The cost price of the article is ________ .

Answer:

₹ 600

Hint:

Given selling price is ₹ 555 & loss 7\(\frac { 1 }{ 2 }\)%

as per formula

(iv) A mixer grinder marked at ₹ 4500 is sold for ₹ 4140 after discount. The rate of discount is ________ .

Answer:

8 %

Hint:

Marked price is ₹ 4500

Discounted price in ₹ 4140

∴ Discount = Marked price – Discounted priòe

= 4500 – 4140 = 360

(v) The total bill amount of a shirt costing ₹ 575 and a T-shirt costing ₹ 325 with GST of 5% is ________ .

Answer:

Cost of price shirt = ₹ 575 (CP)

GST = 5%

Cost of price shirt = ₹ 325 (CP)

GST = 5%

∴ Total bill amount = ₹ 603.75 + ₹ 341.25 = ₹ 945

Question 2.

If selling an article for ₹ 820 causes 10% loss on the selling price, then find its cost price.

Answer:

Given that selling price (SP) = ₹ 820

Loss % = 10 %

Question 3.

If the profit earned on selling an article for ₹ 810 is the same as loss on selling it for ₹ 530, then find the cost price of the article.

Answer:

Case 1: Profit = Selling price (SP) – Cost price (CP)

Case 2: Loss = Cost price (CP) – Selling price (SP)

Given that profit of case 1 = loss of case 2

∴ P = 810 – CP

L = CP – 530

Since profit (P) = loss (L)

810 – CP = CP – 530

∴ 2CP = 810 + 530 = 1340 ⇒ C.P = \(\frac{1340}{2}\)

∴ CP = 670

Question 4.

If the selling price of 10 rulers is the same as the cost price of 15 rulers, then find the profit percentage.

Answer:

Let cost price of one ruler be x

Given that selling price (SP) of 10 rulers.

i.e., same as cost price (CP) of 15 rulers

∴ SP of 10 rulers = 15 × x = 15x

∴ SP of 1 ruler = \(\frac{15 x}{10}\) = 1.5x

∴ Gain = SP of 1 ruler – CP of 1 ruler = 1.5x – x = 0.5x

Question 5.

Some articles are bought at 2 for ₹ 15 and sold at 3 for ₹ 25. Find the gain percentage.

Answer:

Let cost price of one article be C.P

Given that 2 are bought for ₹ 15

∴ 2 × CP = 15 ⇒ CP = \(\frac{15}{2}\)

Let selling price of one article be SP

Given that 3 are sold for ₹ 25

∴ 3 × SP = 25 ⇒ SP = \(\frac{25}{3}\)

∴ Gain = SP – CP = \(\frac{25}{3}-\frac{15}{2}=\frac{50-45}{6}=\frac{5}{6}\)

= \(11 \frac{1}{9}\)

Question 6.

By selling a speaker for ₹ 768, a man loses 20%. In order to gain 20%, how much should he sell the speaker?

Answer:

Selling price (SP) of speaker = ₹ 768

Loss % = 20 %

as per formula

∴ CP = \(\frac{768 \times 100}{80}\) = 960

For gain of 20%, we should now calculate the selling price

= 96 × 12 = ₹ 1152

Question 7.

Find the unknowns x, y and z.

Answer:

(i) Book marked price = ₹ 225 discount 8%

∴ Selling price (x) = Marked price × \(\left(\frac{(100-d \%)}{100}\right)\)

= 225 × \(\frac{(100-8)}{100}\) = 225 × \(\frac{92}{100}\) = ₹ 207

(ii) LED TV selling price = 11970 discount = 5%, Marked price = y

∴ Selling price Marked price y × \(\left(\frac{(100-d \%)}{100}\right)\)

∴ 11970 = y × \(\frac{(100-5)}{100}\)

∴ y = \(\frac{11970 \times 100}{95}\) = 126 × 100 = ₹ 12,600

(iii) Digital clock marked price (MP) = ₹ 750, MP = ₹ 12.600

Selling price (SP) = ₹ 615, Discount = z

100 – z = 82

∴ z = 100 – 82, Discount = 18%

Question 8.

Find the total bill amount for the data given below:

Answer:

Formula for discounted price LW = Marked price (MP) × \(\frac{(100-d \%)}{100}\)

When d is the discount %

For bill amount, we should apply GST on the discounted value of the items.

Formula: Bill amount = Discounted price × \(\left(\frac{(100+\mathrm{GST} \%)}{100}\right)\)

∴ For (i) School bag.

Bill amount 475 × \(\left(\frac{(100+12)}{100}\right)\) = 475 × 1.12 = %‘532

∴ For (ii) Hair drier,

Bill amount = 1800 × \(\left(\frac{(100+28)}{100}\right)\) = 1800 × 1.28 =

∴ Total bill amount Bill amount of School bag + Stationary + Cosmetics + Hair drier

= 532 + 252 + 1357 + 2304

= ₹ 4.445

Question 9.

A branded Air-Conditioner (AC) has a marked price of ₹ 38000. There are 2 options given for the customer.

(i) Selling Price is the same ₹ 38000 but with attractive gifts worth ₹ 3000

(or)

(ii) Discount of 8% on the marked price but no free gifts. Which offer is better?

Answer:

Marked price of AC = ₹ 38,000

Option 1:

Selling price = ₹ 38000 & gifts worth ₹ 3000

∴ Net gain for customer = ₹ 3000 as there is no discount on AC

Option 2:

Discount of 8%, but no gift

∴ Discounted value = MP × \(\left(\frac{(100-d \%)}{100}\right)\)

38000 × \(\frac{(100-8)}{100}\) = 38000 × 0.92 = 34960

∴ Savings for customer = 38000 – 34960 = 3040

Therefore, the customer gets 3000 gift in option I where as he is able to save only ₹ 3040 in option 2. Therefore, option 2 is better.

Question 10.

If a mattress is marked for ₹ 7500 and is available at two successive discount of 10% and 20%, find the amount to be paid by the customer.

Answer:

Marked price of mattress = ₹ 7500

Discount d_{1} = 10%

Discount d_{2} = 20%

Objective Type Questions

Question 11.

A fruit vendor sells fruits for ₹ 200 gaining ₹ 40. His gain percentage is

(A) 20%

(B) 22%

(C) 25%

(D) 16

Answer:

(C) 25%

Hint:

Selling price ₹ 200

Gain = 40

∴ CP – Selling price – gain = 200 – 40 = 160

Question 12.

By selling a flower pot for Z528, a woman gains 20%. At what price should she sell it to gain 25%?

(A) ₹ 500

(B) ₹ 550

(C) ₹ 553

(D) ₹ 573

Answer:

(B) ₹ 550

Hint:

If selling price (sp) = ₹ 528

Gain % = 20 %

∴ CP = ?

Question 13.

A man buys an article for ₹ 150 and makes overhead expenses which are 12% of the cost price. At what price must he sell it to gain 5%?

(A) ₹ 180

(B) ₹ 168

(C) ₹ 176.40

(D) ₹ 88.20

Answer:

(C) ₹ 176.40

Hint:

Cost price of article = ₹ 150

Over head expenses = 12% of cost price

= \(\frac{12}{100}\) × 150 = ₹ 18

∴ Effective cost of article = 150 + 18 = ₹ 168

Now, to gain 5%, he has to sell at

Question 14.

What is the marked price of a hat which is bought for Z210 at 16% discount?

(A) ₹ 243

(B) ₹ 176

(C) ₹ 230

(D) ₹ 250

Answer:

(D) ₹ 250

Hint:

Let marked price be MP

Discounted price = ₹ 210

Rate of discount = 16%

As per formula:

Question 15.

The single discount in % which is equivalent to two successive discounts of 20% and 25% is

(A) 40%

(B) 45%

(C) 5%

(D) 22.5%

Answer:

(A) 40%

Hint:

Let marked price be MP, after discount 1 of 20%,

Comparing with formula, we get

∴ This is equivalent to a single discount of 40%