NCERT Solutions for Class 7 Maths Exercise 7.1 Comparing Quantities

Dive into the world of percentages with these exercises that sharpen your math skills. Percentages show us how big or small one quantity is compared to another. They help us compare discounts, track growth, and split quantities. With these questions, you can convert fractions to percentages to see parts of a whole. You’ll turn decimals into percentages to understand data better.

Find out how to reverse percentages to discover original amounts. Learn to adjust quantities and find the change in areas when dimensions change. Each problem is a step towards mastering percentages. Let’s break down these numerical challenges together. Get ready to become a percentage pro!

NCERT Solutions for Class 7 Maths Exercise 7.1 Chapter 7 Comparing Quantities

1. Convert the given fractional numbers to per cents.

(a) 1/8:
To convert a fraction to a percent, you multiply it by 100.
1/8 = 0.125
0.125 x 100 = 12.5%
So, 1/8 as a percent is 12.5%.

(b) 5/4:
5/4 = 1.25
1.25 x 100 = 125%
So, 5/4 as a percent is 125%.

(c) 3/40:
3/40 = 0.075
0.075 x 100 = 7.5%
So, 3/40 as a percent is 7.5%.

(d) 2/7:
2/7 is approximately 0.2857 (rounded to four decimal places).
0.2857 x 100 = 28.57%
So, 2/7 as a percent is approximately 28.57%.

2. Convert the given decimal fractions to per cents.

(a) 0.65:
0.65 x 100 = 65%
So, 0.65 as a percent is 65%.

(b) 2.1:
2.1 x 100 = 210%
So, 2.1 as a percent is 210%.

(c) 0.02:
0.02 x 100 = 2%
So, 0.02 as a percent is 2%.

(d) 12.35:
12.35 x 100 = 1235%
So, 12.35 as a percent is 1235%.

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

To estimate the part of each figure that is coloured and find the percentage that is coloured, we will look at how many equal sections there are and how many of those sections are coloured.

(i) In the first figure, there are 4 equal sections and 1 of these sections is colored. So, 1 out of 4 parts is colored.
1/4 = 0.25
To find the percent, we multiply by 100:
0.25 x 100 = 25%
Hence, 25% of figure (i) is colored.

(ii) In the second figure, there are 6 equal sections and 3 of these sections are colored. So, 3 out of 6 parts are colored.
3/6 = 0.50
To find the percent, we multiply by 100:
0.50 x 100 = 50%
Hence, 50% of figure (ii) is colored.

(iii) In the third figure, there are 8 equal sections and 3 of these sections are colored. So, 3 out of 8 parts are colored.
3/8 = 0.375
To find the percent, we multiply by 100:
0.375 x 100 = 37.5%
Hence, approximately 37.5% of figure (iii) is colored.

4. Find:

(a) 15% of 250:
To find a percentage of a number, multiply the number by the percentage (as a decimal).
15% of 250 = 0.15 x 250 = 37.5
So, 15% of 250 is 37.5.

(b) 1% of 1 hour:
1 hour is 60 minutes.
1% of 60 minutes = 0.01 x 60 = 0.6 minutes or 1/100 x 60 = 0.6 minutes
So, 1% of 1 hour is 0.6 minutes or 36 seconds.

(c) 20% of ₹ 2500:
20% of 2500 = 0.20 x 2500 = ₹ 500 or 20/100 x 2500 = ₹ 500
So, 20% of ₹ 2500 is ₹ 500.

(d) 75% of 1 kg:
1 kg is 1000 grams.
75% of 1000 grams = 0.75 x 1000 = 750 grams or 75/100 x 1000 = 750 grams
So, 75% of 1 kg is 750 grams.

5. Find the whole quantity if:

(a) 5% of it is 600.
0.05 x Whole Quantity = 600
Whole Quantity = 600 / 0.05
Whole Quantity = 12000

(b) 12% of it is ₹ 1080.
0.12 x Whole Quantity = ₹ 1080
Whole Quantity = ₹ 1080 / 0.12
Whole Quantity = ₹ 9000

(c) 40% of it is 500 km.
0.40 x Whole Quantity = 500 km
Whole Quantity = 500 km / 0.40
Whole Quantity = 1250 km

(d) 70% of it is 14 minutes.
0.70 x Whole Quantity = 14 minutes
Whole Quantity = 14 minutes / 0.70
Whole Quantity = 20 minutes

(e) 8% of it is 40 litres.
0.08 x Whole Quantity = 40 litres
Whole Quantity = 40 litres / 0.08
Whole Quantity = 500 litres

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

(a) 25%
Decimal: 25/100 = 0.25
Fraction: 1/4

(b) 150%
Decimal: 150/100 = 1.50
Fraction: 3/2

(c) 20%
Decimal: 20/100 = 0.20
Fraction: 1/5

(d) 5%
Decimal: 5/100 = 0.05
Fraction: 1/20

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

Step 1: The total percentage of the population, male and female: 30% + 40% = 70%.
Step 2: Since the total population is 100%, the percentage of children: 100% – 70% = 30%.
The percentage of children in the city is 30%.

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?

Step 1: The total percentage of voters who voted is 60%.
Therefore, the percentage of voters who did not vote: 100% – 60% = 40%.

Step 2: The actual number of voters who did not vote.
15,000 voters are in total, and 40% of them did not vote.

Number of voters who did not vote = 40% of 15,000 = (40/100) x 15,000 = 6,000.

40% of the voters did not vote, which is 6,000 voters.

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

Step 1: Meeta saves ₹ 4000, which is 10% of her salary. Let’s denote her total salary as ₹ S.

Step 2: According to the problem, 10% of her salary is ₹ 4000. This can be written as:
10% of ₹ S = ₹ 4000

Step 3: To find her salary, divide ₹ 4000 by 10%:
S = ₹ 4000 / (10/100) = ₹ 4000 / 0.10 = ₹ 40,000.

Therefore, Meeta’s total salary is ₹ 40,000.

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

Step 1: The team played a total of 20 matches and won 25% of them.

Step 2: To find how many matches they won, calculate 25% of 20 matches:
Number of matches won = 25% of 20 = (25/100) x 20 = 5.

The team won 5 matches.

Additional Worksheet Questions for Exercise 7.1 Comparing Quantities

1. If 6% of a number is 54, what is the number?
2. Convert 3/8 into a percent.
3. If the population of a town increases by 25% in a year to reach 25,000, what was it at the beginning of the year?
4. What percent of 2 kilometers is 500 meters?
5. A car decreases in value by 20% per year. If it is worth ₹500,000 now, what was its value last year?
6. In a class of 40 students, 60% are girls. How many boys are in the class?
7. A rectangle’s length is increased by 10% and its width is decreased by 10%. What is the percentage change in the area?
8. A solution contains 30% salt. How much water should be added to 150 liters of the solution to reduce the salt concentration to 15%?
9. If you save 15% of your monthly earnings and this amounts to ₹9,000, what are your monthly earnings?
10. The price of a commodity decreases from ₹75 to ₹60. By what percent has the price decreased?
11. If the side of a square is increased by 20%, by what percent does the area increase?
12. A batch of cookies was shared among 3 children so that the first got 30%, the second got 40%, and the third got the remainder. What percentage of the cookies did the third child get?

Answers

1. The number is 900.
2. 3/8 converted to percent is 37.5%.
3. The population at the beginning of the year was 20,000.
4. 500 meters is 25% of 2 kilometers.
5. The car’s value last year was ₹625,000.
6. There are 16 boys in the class.
7. The area of the rectangle is unchanged, 0% change.
8. 150 liters of water should be added.
9. The monthly earnings are ₹60,000.
10. The price decreased by 20%.
11. The area of the square increases by 44%.
12. The third child got 30% of the cookies.