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

Here are the NCERT Solutions for Class 7 Maths, Exercise 8.2, Chapter 8, Comparing Quantities, in a simple PDF format. These NCERT solutions are very helpful for students to easily clear their doubts and understand the basics of this chapter more effectively.

Key topics covered include comparing quantities using percentages, converting fractions to percentages, converting decimals to percentages, and converting percentages to fractions or decimals. Class 7 students are encouraged to solve these exercises to strengthen their understanding of the concepts and to prepare for exam questions.

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

Question 1. Convert the given fractional numbers to percents:

Solution:

Question 2. Convert the given decimal fractions to per cents:

(а) 0.65

(b) 2.1

(c) 0.02

(d) 12.35

Solution:

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

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

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

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

Question 3. Estimate what part of the figures is coloured and hence find the per cent which is coloured.

Solution:

(i) Fraction of coloured part = \(\frac{1}{4}\)

∴ Percentage of coloured parts 100

(ii) Fraction of coloured part = \(\frac{3}{6}\)

∴ Percentage of coloured parts

(iii) Fraction of coloured part = \(\frac{6}{8}\)

∴ Percentage of coloured parts

Question 4. Find:

(a) 15% of 250

(b) 1% of 1 hour

(c) 20% of ₹ 2500

(d) 75% of 1 kg

Solution:

(a) 15% of 250 = \(\frac{15}{100} \times 250=\frac{75}{2}=37.5\)

(b) 1% of 1 hour = 1% of 60 minutes [∵ 1 h = 60 min.]

 

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

Solution:

Let the required whole quantity be x.

(a) 5% of x = 600

Thus the required whole quantity is 12,000.

(b) 12% of x = ₹ 1080

Thus, the required quantity is ₹ 9,000.

(c) 40% of x = 500 km

Thus, the required quantity = 1250 km.

(d) 70% of x = 14 minutes

Thus, the required quantity = 20 minutes,

(e) 8% of x = 40 litre 8

Thus, the required quantity = 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%

Solution:

 

Question 7. In a city, 30% are females, 40% are males and remaining are children. What per cent are children?

Solution:

Given: 30% are females

40% are males

Total Percentage of females and males

= 30% + 40% = 70%

∴ Percentage of children

= (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?

Solution:

Total number of voters = 15,000

Percentage of the voters who voted = 60%

∴ Percentage of the voters who did not vote

= (100 – 60)% = 40%

Actual number of voters who did not vote

= 40% of 15,000

\(=\frac{40}{100} \times 15,000=6,000\)

Question 9. Meena saves ₹ 400 from her salary. If this is 10% of her salary. What is her salary?

Solution:

Let Meena’s salary by ₹ x.

∴ 10% of x = ₹ 400

Thus, her salary is ₹ 4000.

Question 10. A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?

Solution:

Number of matches played by the cricket team = 20

Percentage of the matches won by them = 25%

i.e. \(\frac{25}{100} \times 20=5\) matches

Thus, the number of matches won by them = 5