Tamilnadu State Board New Syllabus Samacheer Kalvi 8th Maths Guide Pdf Chapter 4 Life Mathematics Ex 4.1 Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 4 Life Mathematics Ex 4.1

Question 1.

Fill in the blanks:

(i) If 30 % of x is 150, then x is _______ .

Answer:

500

Hint:

Given 30% of x is 150

i.e \(\frac{30}{100}\) × x = 150

∴ x = 500

(ii) 2 minutes is _______ % to an hour.

Answer:

3\(\frac{1}{3}\)%

Hint:

Let 2 min be x% of an hour

and 1 hr = 60mm

x% = \(\frac{2}{60} \times 100=\frac{200}{60}=\frac{10}{3}=3 \frac{1}{3}\)

x = 3\(\frac{1}{3}\)%

(iii) If x% of x = 25, then x = _______ .

Answer:

50

Hint:

Given that x% of x is 25

∴ \(\frac{x}{100}\) × x = 25

∴ x^{2} = 25 × 100 = 2500

∴ x = √2500 = 50

(iv) In a school of 1400 students, there are 420 girls. The percentage of boys in the school is _______ .

Answer:

70

Hint:

Given total number of students in school = 1400

Number of girls in school = 420

∴ Number of boys in school = 1400 – 420 = 980

= \(\frac{980}{14}\) = 70

% of boys = 70%

(v) 0.5252 is _______ %.

Answer:

52.52%

Hint:

Given a number, and to express as a percentage, we need to multiply by 100

∴ to express 0.5252 as percentage, we should multiply by 100

∴ 0.5252 × 100 = 52.52%

Question 2.

Rewrite each underlined part using percentage language.

(i) One half of the cake is distributed to the children.

Answer:

50% of the cake is distributed to the children

Hint:

One half is nothing but \(\frac { 1 }{ 2 }\)

as percentage, we need to multiply by 100

∴ \(\frac { 1 }{ 2 }\) × 100 = 50%

(ii) Aparna scored 7.5 points out of 10 in a competition.

Answer:

Aparna scored 75% in a competition

Hint:

7.5 points out of 10 is \(\frac{7.5}{10}\) = 0.75

For percentage, we need to multiply by 100

We get 0.75 × 100 = 75%

(iii) The statue was made of pure silver.

Answer:

The statue was made of 100% pure silver

Hint:

Pure silver means there are no other metals

so, 100 out of 100 parts is made of silver = \(\frac{100}{100}\)

∴ to express as percentage, \(\frac{100}{100}\) × 100% = 100%

(iv) 48 out of 50 students participated in sports.

Answer:

96% students participated in sports.

Hint:

48 out of 50 students in fraction form is \(\frac{48}{50}\)

As a percentage, we need to multiply by 100

(v) Only 2 persons out of 3 will be selected in the interview.

Answer:

Only 66\(\frac{2}{3}\)% will be selected in the interview.

Hint:

2 out of 3 in fraction form is \(\frac{2}{3}\)

to express as percentage, we need to multiply by 100

\(\frac{2}{3} \times 100=\frac{200}{3}=66 \frac{2}{3} \%\)

Question 3.

48 is 32% of which number?

Answer:

Let the number required to be found be ‘x’

Given that 32% of x is 48

i.e., \(\frac{32}{100}\) × x = 48

∴ x = 150

Question 4.

What is 25% of 30% of 400?

Answer:

Required to find 25% of 30% of 400

Question 5.

If a car is sold for ₹ 2,00,000 from its original price of ₹ 3,00,000, then find the percentage of decrease in the value of the car.

Answer:

original price of car = ₹ 3,00,000

actual selling price of car = ₹ 2,00,000

Decrease in amount from original = 3,00,000 – 2,00,000 = 1,00,000

Question 6.

If the difference between 75% of a number and 60% of the same number is 82.5, then find 20% of that number.

Answer:

Given that 75% of number less 60% of number is 82.5

Let the number be ‘x’

∴ \(\frac{75}{100}\) x x – \(\frac{60}{100}\) x x = 82.5

∴ 0.75 x – 0.60 x = 82.5

∴ 0.15 x = 82.5

∴ x = \(\frac{82.5}{0.15}=\frac{8250}{15}\) = 550

Required to find 20% of number ie 20% of x.

Question 7.

A number when increased by 18% gives 236. Find the number.

Answer:

Let the number be x. Given that when it is increased by 18%, we get 236.

Question 8.

A number when decreased by 20% gives 80. Find the number.

Answer:

Let the number be x. Given that when it is increased by 20% we get 80.

x = 100

Question 9.

A number is increased by 25% and then decreased by 20%. Find the percentage change in that number.

Answer:

Method 1.

Let the number be x.

First it is increased by 25%

∴ It becomes x + \(\frac{25}{100}\) × x = \(\frac{125}{100}\)

Secondary it is decreased by 20%

\(\frac{125 x}{100}-\frac{20}{100} \times \frac{125}{100} x=\frac{125}{100} x \times \frac{80}{100}=x\)

Now we get back x, therefore there is no change.

Hence percentage change in that number is 0%

Method 2.

[to understand, let us assume that number is 100]

So, first when we increase by 25%, we get

Now this 125 is decreased by 20%, we get

125 – \(\frac{25}{100}\) × 125 = 125 – 25 = 100

∴ We get back 100 ⇒ No change

Hence percentage change in that number is 0%

Question 10.

The ratio of boys and girls in a class is 5:3. If 16% of boys and 8% of girls failed in an examination, then find the percentage of passed students.

Answer:

Let number of boys be ‘b’ and number of girls be ‘g’

Ratio of boys and girls is given as 5:3

b:g = 5:3 ⇒ \(\frac{b}{g}=\frac{5}{3}\) …… (A)

Failure in boys = 16% = \(\frac{16}{100}\) × b = \(\frac{16b}{100}\)

Failure in girls = 8% = \(\frac{8}{100}\) × g = \(\frac{8g}{100}\)

Pass in boys = 100 – 16% = 84% = \(\frac{84}{100} b\) …… (1)

Pass in girls = 100 – 8% = 92% = \(\frac{92}{100} g\) ……. (2)

From A, we have \(\frac{b}{g}=\frac{5}{3}\) , adding I on both sides, we get

\(\frac{b}{g}\) + 1 = \(\frac{5}{3}\) + 1

\(\frac{b+g}{g}=\frac{5+3}{3}=\frac{8}{3}\)

∴ g = \(\frac{3}{8}\)(b + g) ……. (3)

Similarly b = \(\frac{5}{8}\) (b + g) ……. (4)

Total pass = pass in girls + pass in boys

= (1) + (2) = \(\frac{84}{100} b+\frac{92}{100} g\)

Objective Type Questions

Question 11.

12% of 250 litre is the same as ________ of 150 litre.

(A) 10%

(B) 15%

(C) 20%

(D) 30%

Answer:

(C) 20%

Hint:

12% of 250 = \(\frac{12}{100}\) × 250 = 30 lit.

Percentage: \(\frac{30}{150}\) × 100 = 20%

Question 12.

If three candidates A, B and C in a school election got 153,245 and 102 votes respectively, then the percentage of votes got by the winner is ________ .

(A) 48%

(B) 49%

(C) 50%

(D) 45%

Answer:

(B) 49%

Hint:

Candidate 1: 153

Candidate 2: 245 – winner [as maximum votes)

Candidate 3: 102

Total votes = 1 + 2 + 3 = 153 + 245 + 102 = 500

= \(\frac{245}{500}\) × 100 = 49%

Question 13.

15% of 25% of 10000 = ________ .

(A) 375

(B) 400

(C) 425

(D) 475

Answer:

(A) 375

Hint:

15% of 25% of 10000 is

First let us do 25% of 10,000, which is

Next 15% of the above is \(\frac{15}{100}\) × 2500 = 375

Question 14.

When 60 is subtracted from 60% of a number to give 60, the number is

(A) 60

(B) 100

(C) 150

(D) 200

Answer:

(D) 200

Hint:

Let the number be ‘X’

60% of the number is \(\frac{60}{100}\) × x = \(\frac{60x}{100}\)

Given that when 60 is subtracted from 60%, we get 60

i.e \(\frac{60}{100}\) x – 60 = 60

∴ \(\frac{60}{100}\) x 60 + 60 = 120

∴ x = \(\frac{120 \times 100}{60}\) = 200

Question 15.

If 48% of 48 = 64% of x, then x =

(A) 64

(B) 56

(C) 42

(D) 36

Answer:

(D) 36

Hint:

Given that 48% of 48 = 64% of x

x = 36