These NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.2 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Exercise 8.2

Question 1.

Convert the given fractional numbers to per cents

(i) \(\frac{1}{9}\)

(b) \(\frac{5}{4}\)

(c) \(\frac{3}{40}\)

(d) \(\frac{2}{7}\)

Answer:

Question 2.

Convert the given decimal fractions to per cents.

(a) 0.65

(b) 2.1

(c) 0.02

(d) 12.35

Answer:

(a) 0.65 : \(\frac{64}{100}=\frac{65}{100}\) × 100% = 65%

(b) 2.1 = \(\frac{21}{10}=\frac{21}{10}\) × 100% = 210%

(c) 0.02 = \(\frac{2}{100}=\frac{2}{100}\) × 100% =2 %

(d) 12.35 = \(\frac{1235}{100}=\frac{1235}{100}\) × 100% = 1235

Question 3.

Estimate what part of the figures is shaded and hence find the per cent which is shaded.

Answer:

(i) \(\frac{1}{4}\) part is shaded.

\(\frac{1}{4}=\frac{1}{4}\) × 100% = % = 25 %

This coloured part is 25%.

(ii) 3 parts out of 5 parts are shaded so,

\(\frac{3}{5}\) part is shaded

\(\frac{3}{5}=\frac{3}{5}\) × 100% = 3 × 20% = 60%

This coloured part is 60%.

(iii) Here 3 parts out of 8 parts are shaded 3

so, \(\frac{3}{8}\) part is shaded.

\(\frac{3}{8}=\frac{3}{8}\) × 100% = \(\frac{3}{2}\) x 25%

= 37\(\frac { 1 }{ 2 }\)% or 37.5%

This 37\(\frac { 1 }{ 2 }\) part is shaded.

Question 4.

Find:

(a) 15% of 250

(b) 1% of 1 hour

(c) 20% of ₹ 2500

(d) 75% of 1 kg

Answer:

(a) 15% of 250 = \(\frac{15}{100}\) of 250

= \(\frac{15}{100} \times 250=\frac{15 \times 250}{100}=\frac{75}{2}\)

= 37\(\frac{1}{2}\) or 37.5

∴ 15% of 250 = 37 \(\frac{1}{2}\) or 37.5 2

(b) 1% of 1 hour = \(\frac{1}{100}\) × 60 minutes

= \(\frac{1 \times 60}{100}=\frac{3}{5}\) minutes

= \(\frac { 3 }{ 5 }\) × 60 seconds = 36 seconds

∴ 1% of 1 hour = 36 seconds

(c) 20% of ₹ 2500 = \(\frac { 20 }{ 100 }\) of

2500 = \(\frac { 20 }{ 100 }\) x 2500

= ₹ \(\frac{20 \times 2500}{100}\) = ₹ 500

∴ 20% of ₹ 2500 = ₹ 500

(d) 75% of 1 kg = 75% of 1000 g

= \(\frac{75}{100} \times 100 \mathrm{~g}=\frac{75 \times 1000}{100}\) = 750 g

∴ 75% of 1 kg = 750g

Question 5.

Find the whole quantity if

(a) 5% of it is 600.

(b) 12% of it is ₹ 1080.

(c) 40% of it is 500 km.

(d) 70% of it is 14 minutes.

(e) 8% of it is 40 litres.

Answer:

(a) 5% of a quantity is 600.

Let the quantity be x

5% of x = 600

\(\frac { 5 }{ 100 }\) × x = 600

x = \(\frac{600 \times 100}{5}\)

= 120 × 100

= 12000

Thus the required quantity is 12000.

(b) 12% of it is ₹ 1080

Let the required amount be x

12% of x = 1080

\(\frac { 12 }{ 100 }\) × x = 1080

x = \(\frac{1080 \times 100}{12}\)

= \(\frac{1080 \times 25}{3}\)

The required amount = ₹ 9000

= 360 × 25 = ₹ 9000

(c) 40% of it is 500 km

Let the total quantity be x

40% of x = 500

\(\frac { 4 }{ 100 }\) × x = 500

x = \(\frac{500 \times 100}{40}\) km

= 50 × 25 km

= 1250 km

The required quantity is 1250 km.

(d) 70% of it is 14 minutes

Let the required time be x

70% of x = 14 minutes

\(\frac{70}{100}\) × x = 14

x = \(\frac{14 \times 100}{70}\)

= 20 minutes

Thus, the required quantity is 20 minutes.

(e) 8% of a quantity is 40 litres

Let the quantity be x

8% of x =40 litres

\(\frac { 8 }{ 100 }\) × x = 40

x = \(\frac{40 \times 100}{8}\) = 500litres

The required quantity is 500 litres.

Question 6.

Convert given per cents to decimal fractions and also to fractions in simplest forms:

(a) 25%

(b) 150%

(c) 20%

(d) 5%

Answer:

(a) 25% = \(\frac{25}{100}=\frac{1}{4}\)

Thus, 20% = \(\frac{1}{4}\) = 0.25

(b) 150% = \(\frac{150}{100}=\frac{3}{2}\)

Thus 150% = \(\frac{3}{2}\) (or) 1\(\frac{1}{2}\) = 1.5

(c) 20% = \(\frac{20}{100}=\frac{1}{5}\) = 0.2

Thus 20% = \(\frac{1}{5}\) = 0.2

(d) 5% = \(\frac{5}{100}=\frac{1}{20}\)

Thus 5% = \(\frac{1}{20}\) = 0.05

Question 7.

In a city, 30% are females, 40% are males and remaining are children. What per cent are children?

Answer:

Females are 30% and males are 40%

Number of children = 100% – (30% + 40%)

= 100% – 70% = 30%

Thus, children are 30% of the population.

Question 8.

Out of 15,000 voters in a constituency, 60% voted. Find the percentage of voters who did not vote. Can you now find how many actually did not vote?

Answer:

Total number of voters = 15,000

Part of voters who voted = 60%

Part of voters who did not vote = 100% – 60% = 40%

40% of 15000 = \(\frac{40}{100}\) × 15000

= 40 × 150 = 6000

Thus, 6000 voters did not vote.

Question 9.

Meeta saves ₹ 4000 from her salary. If this is 10% of her salary. What is her salary?

Answer:

Meeta saving = ₹ 4000

Let the salary be ₹ x

Saving = 10% of x

10% of x =4000

\(\frac{10}{100}\) × x = 4000

x = \(\frac{4000 \times 100}{10}\)

= ₹ 40,000

Meeta salary = ₹ 40,000/-

Question 10.

A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?

Answer:

Total number of matches played = 20

Part of matches won = 25%

25% of 20 = \(\frac{25}{100}\) × 20 = \(\frac{25 \times 20}{100}\) = 5

The team won 5 matches.