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.