RBSE Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.2

Rajasthan Board RBSE Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.2 Textbook Exercise Questions and Answers.

RBSE Class 7 Maths Solutions Chapter 8 Comparing Quantities Ex 8.2

Question 1. 
Convert the given fractional numbers to percents:
(a) \(\frac{1}{8}\)
Answer:
\(\frac{1}{8}=\frac{1}{8}\) × 100 % = \(\frac{25}{2}\)% or 12.5%

(b) \(\frac{5}{4}\)
Answer:
\(\frac{5}{4}=\frac{5}{4}\) × 100 % = 5 × 25 % = 125 %

(c) \(\frac{3}{40}\)
Answer:
\(\frac{3}{40}=\frac{3}{40}\) × 100 % = \(\frac{15}{2}\) % = 7.5%

(d) \(\frac{2}{7}\)
Answer:
\(\frac{2}{7}=\frac{2}{7}\) × 100 % = \(\frac{200}{7}\)% = 28\(\frac{4}{7}\)%

Question 2.
Convert the given decimal frac¬tions to percentages:
(a) 0.65
Answer:
0.65 = \(\frac{65}{100}\)= \(\frac{65}{100}\) × 100% = 65%

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

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

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

Question 3.
Estimate what part of the figures is coloured and hence find the percent which is coloured?

Answer:
(i) \(\frac{1}{4}\) part is coloured, i.e.
\(\frac{1}{4}\) × 100% = 25%
∴ 25 percent part is coloured

(ii) \(\frac{3}{5}\) part is coloured i.e.
\(\frac{3}{5}\) × 100% = 60%
∴ 60 percent part is coloured

(ii) \(\frac{3}{8}\) part is coloured i.e.
\(\frac{3}{8}\) × 100% = \(\frac{75}{2}\)% = 37.5%
∴ 37.5 percent part is coloured

Question 4.
(a) 15% of 250
Answer:
15% of 250 = \(\frac{15}{100}\) × 250 = \(\frac{75}{2}\) = 37.5

(b) 1% of 1 hour
Answer:
1% of 1 hour = \(\frac{1}{100}\) × 1 hour = \(\frac{60}{100}\) minute
= \(\frac{3}{5}\) minute = \(\frac{3}{5}\) × 60 second = 36 second

(c) 20% of ₹ 2500
Answer:
20% of ₹ 2500 = ₹ \(\frac{20}{100}\) × 250 = ₹ 500

(d) 75% of 1 kg
Answer:
75% of 1 kg = \(\frac{75}{100}\) × 1 kg = \(\frac{3}{4}\) kg
= \(\frac{3}{4}\) × 1000 g = 750 g = 0.750 kg

Question 5.
Find the whole quantity, if:
(a) 5% of it is 600
Answer:
Let the whole quantity be A.
∴ 5% of A = 600
⇒ \(\frac{5}{100}\) × A = 600 ⇒ \(\frac{A}{20}\) = 600 ⇒ A = 12000
∴ The whole quantity is 12000.

(b) 12% of it is ₹ 1080
Answer:
Let the whole quantity be ₹ A.
∴ 12% of ₹ A = ₹ 1080
⇒ \(\frac{12 \times \mathrm{A}}{100}\) = ₹ 1080 ⇒ \(\frac{3 A}{25}\) = ₹ 1080
⇒ A = \(\frac{1080 \times 25}{3}\)
⇒ A = ₹ 9000
∴ The whole quantity is 9000.

(c) 40% of it is 500 km
Answer:
Let the whole quantity be A km.
∴ 40% of A = 500
⇒ \(\frac{40 \times A}{100}\) = 500
⇒ \(\frac{2 A}{5}\) = 500
∴ The whole quantity be 1250 km.

(d) 70% of it is 14 minute
Answer:
Let the whole quantity be A minutes. 
∴ 70% of A = 14
⇒ \(\frac{70}{100}\) × A = 14 
⇒ \(\frac{7 A}{10}\) = 14
⇒ A = \(\frac{14 \times 10}{7}\) ⇒ A = 20
∴ The whole quantity is 20 minutes

(e) 8% of it is 40 litre
Answer:
Let the whole quantity be A litres.
∴8% of A = 40
⇒ \(\frac{8}{100}\) × A = 40
⇒ \(\frac{2 A}{25}\) = 40
⇒  A = \(\frac{40 \times 25}{2}\) ⇒ A = 500
∴ The whole quantity is 500 litres.

Question 6.
Convert given percents to decimal fractions and also to fractions in simplest forms:
(a) 25%
Answer:
25% = \(\frac{25}{100}\) = 0.25 = \(\frac{5}{20}=\frac{1}{4}\)

(b) 150%
Answer:
150% = \(\frac{150}{100}\) = 1.50 = \(\frac{3}{2}\)

(c) 20%
Answer:
20% = \(\frac{20}{100}\) = 0.20 = \(\frac{1}{5}\)

(d) 5%
Answer:
5% = \(\frac{5}{100}\) = 0.05 = \(\frac{1}{20}\)

Question 7.
In a city, 30% are females, 40% are males and remaining are children. What percent are children?
Answer:
Total population of city = 100% 
Population of females = 30% 
Population of males = 40%
∴ Population of children
= [100% - (30% + 40%)]
= 100% - 70% = 30%

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:
40% of voters did not vote (100% - 60%).
Number of voters who actually did not vote
= 40% of 15,000 = \(\frac{40}{100}\) × 15,000 = 6,000 
Hence 6000 candidates did not vote.

Question 9. 
Meeta saves ₹ 4,000 from her salary. If this is 10% of her salary. What is her salary?
Answer:
Let the total salary of Meeta be ₹ A.
10% of A = 4,000 ⇒ \(\frac{10}{100}\) × A = ₹ 4,000
⇒ \(\frac{A}{10}\) = 4,000
⇒ A = 4,000 × 10 ⇒ A = ₹ 40,000
∴ Total 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:
Let the total number of matches won be A. Then,
25% of 20 = A
⇒ \(\frac{25}{100}\) × 20 = A ⇒ A = 5
∴ They won 5 matches.