NCERT Solutions for Class 7 Maths Exercise 8.2

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NCERT solutions for Maths Comparing Quantities Download as PDF

NCERT Solutions for Class 7 Maths Comparing Quantities

Class –VII Mathematics (Ex. 8.2)

Question 1.Convert the given fractional numbers to percent:

(a) {tex}\frac{1}{8}{/tex}

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

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

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

Answer:

(a) {tex}\frac{1}{8}{/tex} = {tex}\frac{1}{8} \times 100\% = \frac{{25}}{2}\% {/tex} = 12.5%

(b) {tex}\frac{5}{4}{/tex} = {tex}\frac{5}{4} \times 100\% = {/tex} 5 x 25% = 125%

(c) {tex}\frac{3}{{40}}{/tex} = {tex}\frac{3}{{40}} \times 100\% = \frac{3}{2} \times 5\% = \frac{{15}}{2}\% {/tex} = 7.5%

(d) {tex}\frac{2}{7}{/tex} = {tex}\frac{2}{7} \times 100\% = \frac{{200}}{7}\% = 28\frac{4}{7}\% {/tex}

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NCERT Solutions for Class 7 Maths Exercise 8.2

Question 2.Convert the given decimal fractions to percents:

(a) 0.65

(b) 2.1

(c) 0.02

(d) 12.35

Answer:

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

(b) 0.02 = {tex}\frac{2}{{100}} \times 100\% {/tex} = 2%

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NCERT Solutions for Class 7 Maths Exercise 8.2

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

Answer:

(i) Coloured part = {tex}\frac{1}{4}{/tex}

{tex}\therefore {/tex} Percent of coloured part = {tex}\frac{1}{4} \times 100\% {/tex} = 25%

(ii) Coloured part = {tex}\frac{3}{5}{/tex}

{tex}\therefore {/tex} Percent of coloured part = {tex}\frac{3}{5} \times 100\% {/tex} = 60%

(iii) Coloured part = {tex}\frac{3}{8}{/tex}

{tex}\therefore {/tex} Percent of coloured part = {tex}\frac{3}{8} \times 100\% {/tex} = {tex}\frac{3}{2} \times 25\% {/tex}

= 37.5%

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Question 4.Find:

(a) 15% of 250

(b) 1% of 1 hour

(c) 20% of Rs. 2500

(d) 75% of 1 kg

Answer:

(a) 15% of 250 = {tex}\frac{{15}}{{100}} \times 250{/tex} = 15 x 2.5 = 37.5

(b) 1% of 1 hours = 1% of 60 minutes = 1% of (60 x 60) seconds

= {tex}\frac{1}{{100}} \times 60 \times 60{/tex} = 6 x 6 = 36 seconds

(c) 20% of Rs. 2500 = {tex}\frac{{20}}{{100}} \times 2500{/tex} = 20 x 25 = Rs. 500

(d) 75% of 1 kg = 75% of 1000 g = {tex}\frac{{75}}{{100}} \times 1000{/tex} = 750 g = 0.750 kg

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NCERT Solutions for Class 7 Maths Exercise 8.2

Question 5.Find the whole quantity if:

(a) 5% of it is 600

(b) 12% of it is Rs. 1080

(c) 40% of it is 500 km

(d) 70% of it is 14 minutes

(e) 8% of it is 40 liters

Answer:

Let the whole quantity be {tex}x{/tex} in given questions:

(a) 5% of {tex}x{/tex} = 600 {tex} \Rightarrow {/tex} {tex}\frac{5}{{100}} \times x = 600{/tex}

{tex} \Rightarrow {/tex} {tex}x = \frac{{600 \times 100}}{5}{/tex} = 12,000

(b) 12% of {tex}x{/tex} = Rs. 1080 {tex} \Rightarrow {/tex}{tex}\frac{{12}}{{100}} \times x = 1080{/tex}

{tex} \Rightarrow {/tex} {tex}x = \frac{{1080 \times 100}}{{12}}{/tex} = Rs. 9,000

(c) 40% of {tex}x{/tex} = 500 km {tex} \Rightarrow {/tex} {tex}\frac{{40}}{{100}} \times x = 500{/tex}

{tex} \Rightarrow {/tex} {tex}x = \frac{{500 \times 100}}{{40}}{/tex} = 1,250 km

(d) 70% of {tex}x{/tex} = 14 minutes {tex} \Rightarrow {/tex} {tex}\frac{{70}}{{100}} \times x = 14{/tex}

{tex} \Rightarrow {/tex} {tex}x = \frac{{14 \times 100}}{{70}}{/tex} = 20 minutes

(e) 8% of {tex}x{/tex} = 40 liters {tex} \Rightarrow {/tex} {tex}\frac{8}{{100}} \times x = 40{/tex}

{tex} \Rightarrow {/tex} {tex}x = \frac{{40 \times 100}}{8}{/tex} = 500 liters

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NCERT Solutions for Class 7 Maths Exercise 8.2

Question 6.Convert given percents to decimal fractions and also to fractions in simplest forms:

(a) 25%

(b) 150%

(c) 20%

(d) 5%

Answer:

S. No.	Percents	Fractions	Simplest form	Decimal form
(a)	25%	{tex}\frac{{25}}{{100}}{/tex}	{tex}\frac{1}{4}{/tex}	0.25
(b)	150%	{tex}\frac{{150}}{{100}}{/tex}	{tex}\frac{3}{2}{/tex}	1.5
(c)	20%	{tex}\frac{{20}}{{100}}{/tex}	{tex}\frac{1}{5}{/tex}	0.2
(d)	5%	{tex}\frac{5}{{100}}{/tex}	{tex}\frac{1}{{20}}{/tex}	0.05

NCERT Solutions for Class 7 Maths Exercise 8.2

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

Answer:

Given: Percentage of females = 30%

Percentage of males = 40%

Total percentage of females and males = 30 + 40 = 70%

Percentage of children = Total percentage – Percentage of males and females

= 100% – 70%

= 30%

Hence, 30% are children.

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NCERT Solutions for Class 7 Maths Exercise 8.2

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 voters = 15,000

Percentage of voted candidates = 60%

Percentage of not voted candidates = 100 – 60 = 40%

Actual candidates, who did not vote = 40% of 15000

= {tex}\frac{{40}}{{100}} \times 15000{/tex} = 6,000

Hence, 6,000 candidates did not vote.

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NCERT Solutions for Class 7 Maths Exercise 8.2

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

Answer:

Let Meera’s salary be Rs.{tex}x.{/tex}

Now, 10% of salary = Rs. 400

{tex} \Rightarrow {/tex} 10% of {tex}x{/tex} = Rs. 400

{tex} \Rightarrow {/tex} {tex}\frac{{10}}{{100}} \times x = 400{/tex}

{tex} \Rightarrow {/tex} {tex}x = \frac{{400 \times 100}}{{10}}{/tex}

{tex} \Rightarrow {/tex} {tex}x = {/tex} 4,000

Hence, Meera’s salary is Rs. 4,000.

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NCERT Solutions for Class 7 Maths Exercise 8.2

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

Answer:

Number of matches played by cricket team = 20

Percentage of won matches = 25%

Total matches won by them = 25% of 20

= {tex}\frac{{25}}{{100}} \times 20{/tex}

= 5

Hence, they won 5 matches.

NCERT Solutions for Class 7 Maths Exercise 8.2

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