## NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities (EX 8.2) Exercise 8.2

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## Access NCERT Solutions for Class 7 Maths Chapter 8 – Comparing Quantities

Exercise 8.2

1. Convert the given fractional numbers to percent:

a) The fraction is \[\dfrac{1}{8}\].

Ans: Converting a fraction into percentage is multiplying the given fraction by $100\% $.

The given fraction is $\dfrac{1}{8}$.

Multiply the given fraction by $100\% $ and simplify to obtain the equivalent percentage.

$\dfrac{1}{8} \times 100\% = \dfrac{{25}}{2}\% $

$\dfrac{1}{8} \times 100\% = 12.5\% $

Therefore, the fractional number $\dfrac{1}{8}$ is equivalent to $12.5\% $.

b) The fraction is \[\dfrac{5}{4}\].

Ans: Converting a fraction into percentage is multiplying the given fraction by $100\% $.

The given fraction is \[\dfrac{5}{4}\].

Multiply the given fraction by $100\% $ and simplify to obtain the equivalent percentage.

$\dfrac{5}{4} \times 100\% = 5 \times 25\% $

$\dfrac{5}{4} \times 100\% = 125\% $

Therefore, the fractional number \[\dfrac{5}{4}\] is equivalent to $125\% $.

c) The fraction is \[\dfrac{3}{{40}}\].

Ans: Converting a fraction into percentage is multiplying the given fraction by $100\% $.

The given fraction is \[\dfrac{3}{{40}}\].

Multiply the given fraction by $100\% $ and simplify to obtain the equivalent percentage.

$\dfrac{3}{{40}} \times 100\% = \dfrac{{3 \times 5}}{2}\% $

$\dfrac{3}{{40}} \times 100\% = 7.5\% $

Therefore, the fractional number \[\dfrac{3}{{40}}\] is equivalent to $7.5\% $.

d) The fraction is \[\dfrac{2}{7}\].

Ans: Converting a fraction into percentage is multiplying the given fraction by $100\% $.

The given fraction is \[\dfrac{2}{7}\].

Multiply the given fraction by $100\% $ and simplify to obtain the equivalent percentage.

$\dfrac{2}{7} \times 100\% = \dfrac{{200}}{7}\% $

$\dfrac{2}{7} \times 100\% = 28\dfrac{4}{7}\% $

$\dfrac{2}{7} \times 100\% = 28.571428...$

Therefore, the fractional number \[\dfrac{2}{7}\] is equivalent to $28\dfrac{4}{7}\% $ or $28.571428..\% $.

2. Convert the given decimal fractions to percents:

a) The number is $0.65$

Ans: The decimal number given is $0.65$.

The given decimal number can also be written in $\dfrac{p}{q}$ form as, $\dfrac{{65}}{{100}}$.

Now, converting a fraction into percentage is multiplying the given fraction by $100\% $.

Multiply the given fraction by $100\% $ and simplify to obtain the equivalent percentage.

$\dfrac{{65}}{{100}} \times 100\% = 65\% $

Therefore, the decimal number \[0.65\] is equivalent to $65\% $.

b) The number is $2.1$

Ans: The decimal number given is $2.1$.

The given decimal number can also be written in $\dfrac{p}{q}$ form as, $\dfrac{210}{{100}}$.

Now, converting a fraction into percentage is multiplying the given fraction by $100\% $.

Multiply the given fraction by $100\% $ and simplify to obtain the equivalent percentage.

$\dfrac{210}{{100}} \times 100\% = 210\% $

Therefore, the decimal number \[2.1\] is equivalent to $210\% $.

(c) The number is $0.02$

Ans: The decimal number given is $0.02$.

The given decimal number can also be written in $\dfrac{p}{q}$ form as, $\dfrac{2}{100}$.

Now, converting a fraction into percentage is multiplying the given fraction by $100%$.

Multiply the given fraction by $100%$ and simplify to obtain the equivalent percentage.

$\dfrac{2}{100}\times 100%=2\%$

Therefore, the decimal number $0.02$ is equivalent to $2\%$.

(d) The number is $12.35$.

Ans: The decimal number given is $12.35$.

The given decimal number can also be written in $\dfrac{p}{q}$ form as, $\dfrac{1235}{100}$.

Now, converting a fraction into percentage is multiplying the given fraction by $100%$.

Multiply the given fraction by $100%$ and simplify to obtain the equivalent percentage.

$\dfrac{1235}{100}\times 100%= 1235\%$

Therefore, the decimal number $12.35$ is equivalent to $1235\%$.

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

i) The given figure is,

(Image Will Be Updated Soon)

Ans: The given figure has a circle with a shaded portion.

From the given figure, it can be estimated that the colored part of the circle is the ${\dfrac{1}{4}^{th}}$ portion.

Hence, ${\text{The colored portion}} = \dfrac{1}{4}$.

Now, to find the percentage of the colored portion, convert the obtained fraction of the colored portion into percentage. This can be done by multiplying the fraction by $100\% $ and then simplifying.

Thus,

\[{\text{The percent of colored portion}} = \dfrac{1}{4} \times 100\% \]

\[{\text{The percent of colored portion}} = \dfrac{{100}}{4}\% \]

\[{\text{The percent of colored portion}} = 25\% \]

Therefore, the percent of the colored part from the given figure is found to be $25\% $.

ii) The given figure is,

(Image Will Be Updated Soon)

Ans: The given figure has a circle with a shaded portion.

The figure shows that the circle is divided into 5 equal parts.

Thus, it can be estimated that the colored part of the circle is the ${\dfrac{3}{5}^{th}}$ portion.

Hence, ${\text{The colored portion}} = \dfrac{3}{5}$.

Now, to find the percentage of the colored portion, convert the obtained fraction of the colored portion into percentage. This can be done by multiplying the fraction by $100\% $ and then simplifying.

Thus,

\[{\text{The percent of colored portion}} = \dfrac{3}{5} \times 100\% \]

\[{\text{The percent of colored portion}} = \dfrac{{300}}{5}\% \]

\[{\text{The percent of colored portion}} = 60\% \]

Therefore, the percent of the colored part from the given figure is found to be $60\% $.

iii) The given figure is,

(Image Will Be Updated Soon)

Ans: The given figure has a circle with a shaded portion.

The figure shows that the circle is divided into 8 equal parts.

Thus, it can be estimated that the colored part of the circle is the ${\dfrac{3}{8}^{th}}$ portion.

Hence, ${\text{The colored portion}} = \dfrac{3}{8}$.

Now, to find the percentage of the colored portion, convert the obtained fraction of the colored portion into percentage. This can be done by multiplying the fraction by $100\% $ and then simplifying.

Thus,

\[{\text{The percent of colored portion}} = \dfrac{3}{8} \times 100\% \]

\[{\text{The percent of colored portion}} = \dfrac{{300}}{8}\% \]

\[{\text{The percent of colored portion}} = 37.5\% \]

Therefore, the percent of the colored part from the given figure is found to be $37.5\% $.

4. Find the percentage of the following:

a) $15\% {\text{ }}$of 250

Ans: The number given is 250.

The percentage of any number $n$, that is $n\% $, is written as $\dfrac{n}{{100}}$.

$15\% $ is also represented in fraction form as, $\dfrac{{15}}{{100}}$.

Therefore, $15\% $ of 250 is represented as $\dfrac{{15}}{{100}} \times 250$.

Evaluate the above expression.

$\dfrac{{15}}{{100}} \times 250 = 15 \times 2.5$

$\dfrac{{15}}{{100}} \times 250 = 37.5$

Therefore, $15\% {\text{ of 250}}$ is found to be $37.5$.

b) $1\% $ of 1 hours.

Ans: It is known that 1 hours is 60 minutes.

Also, 60 minutes is equal to $\left( {60 \times 60} \right)$ seconds.

The percentage of any number $n$, that is $n\% $, is written as $\dfrac{n}{{100}}$.

Thus, finding $1\% $ of 1 hours is to find $1\% $ of $\left( {60 \times 60} \right)$ seconds. $1\% $ is also represented as $\dfrac{1}{{100}}$.

Hence,

$1\% {\text{ of }}\left( {60 \times 60} \right){\text{ seconds}} = \dfrac{1}{{100}}\left( {60 \times 60} \right){\text{ seconds}}$.

$1\% {\text{ of }}\left( {60 \times 60} \right){\text{ seconds}} = \dfrac{{3600}}{{100}}{\text{ seconds}}$.

$1\% {\text{ of }}\left( {60 \times 60} \right){\text{ seconds}} = 36{\text{ seconds}}$.

c) $20\% $ of ₹2500

Ans: The amount given is ₹2500.

The percentage of any number $n$, that is $n\% $, is written as $\dfrac{n}{{100}}$.

$20\% $ is also represented in fraction form as, $\dfrac{{20}}{{100}}$.

Therefore, $20\% $ of 2500 is represented as $\dfrac{{20}}{{100}} \times 2500$.

Evaluate the above expression.

$\dfrac{{20}}{{100}} \times 2500 = 20 \times 25$

$\dfrac{{20}}{{100}} \times 2500 = 500$

Therefore,$20\% $ of ₹2500 is found to be ₹500.

d) $75\% $ of 1kg

Ans: It is known that 1 kg is 1000g.

The percentage of any number $n$, that is $n\% $, is written as $\dfrac{n}{{100}}$.

$75\% $ is also represented in fraction form as, $\dfrac{{75}}{{100}}$.

Therefore, $75\% $ of 1000 is represented as $\dfrac{{75}}{{100}} \times 1000$.

Evaluate the above expression.

$\dfrac{{75}}{{100}} \times 1000 = 750{\text{g}}$

Thus,

$750{\text{ g}} = \dfrac{{750}}{{1000}}{\text{ kg}}$

$750{\text{ g}} = 0.75{\text{ kg}}$

Therefore, $75\% $ of 1kg is found to be $0.75{\text{ kg}}$.

5. Find the whole quantity if:

a) $5\% $ of it is 600

Ans: Let $x$ be the assumed quantity.

The percentage of any number $n$, that is $n\% $, is written as $\dfrac{n}{{100}}$.

$5\% $ of $x$ can be represented as $\dfrac{5}{{100}}$ of $x$ which is equal to 600.

This can be formulated as follows,

$5\% {\text{ of }}x = 600$

Thus,

$\dfrac{5}{{100}} \times x = 600$

Evaluate further,

$x = \dfrac{{600 \times 100}}{5}$

$x = \dfrac{{60000}}{5}$

$x = 12000$

Therefore, the quantity is found to be 12000.

b) $12\% $ of it is ₹ 1080.

Ans: Let $x$ be the assumed quantity.

The percentage of any number $n$, that is $n\% $, is written as $\dfrac{n}{{100}}$.

$12\% $ of $x$ can be represented as $\dfrac{{12}}{{100}}$ of $x$ which is equal to ₹1080.

This can be formulated as follows,

$12\% {\text{ of }}x = 1080$

Thus,

$\dfrac{{12}}{{100}} \times x = 1080$

Evaluate further,

$x = \dfrac{{1080 \times 100}}{{12}}$

$x = \dfrac{{108000}}{{12}}$

$x = 9000$

Therefore, the quantity is found to be ₹9000.

c) $40\% $ of it is 500 km.

Ans: Let the assumed quantity be $x$.

The percentage of any number $n$, that is $n\% $, is written as $\dfrac{n}{{100}}$.

$40\% $ of $x$ can be represented as $\dfrac{{40}}{{100}}$ of $x$ which is equal to 500 km.

This can be formulated as follows,

$40\% {\text{ of }}x = 500{\text{ km}}$

Thus,

$\dfrac{{40}}{{100}} \times x = 500$

Evaluate further,

$x = \dfrac{{500 \times 100}}{{40}}$

$x = \dfrac{{50000}}{{40}}$

$x = 1,250{\text{ km}}$

Therefore, the quantity is found to be 1,250 km.

d) $70\% $ of it is 14 minutes

Ans: Let the assumed quantity be $x$.

The percentage of any number $n$, that is $n\% $, is written as $\dfrac{n}{{100}}$.

$70\% $ of $x$ can be represented as $\dfrac{{70}}{{100}}$ of $x$ which is equal to 14 minutes.

This can be formulated as follows,

$70\% {\text{ of }}x = 14{\text{ minutes}}$

Thus,

$\dfrac{{70}}{{100}} \times x = 14$

Evaluate further,

$x = \dfrac{{14 \times 100}}{{70}}$

$x = \dfrac{{1400}}{{70}}$

$x = 20{\text{ minutes}}$

Therefore, the quantity is found to be 20 minutes.

e) $8\% $ of it is 40 liters

Ans: Let the assumed quantity be $x$.

The percentage of any number $n$, that is $n\% $, is written as $\dfrac{n}{{100}}$.

$8\% $ of $x$ can be represented as $\dfrac{8}{{100}}$ of $x$ which is equal to 40 liters.

This can be formulated as follows,

$8\% {\text{ of }}x = 40{\text{ liters}}$

Thus,

$\dfrac{8}{{100}} \times x = 40$

Evaluate further,

$x = \dfrac{{40 \times 100}}{8}$

$x = \dfrac{{4000}}{8}$

$x = 500$

Therefore, the quantity is found to be 500 liters.

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

a) The percentage is $25\% $.

Ans: The percentage of any number $n$, that is $n\% $, is written as $\dfrac{n}{{100}}$.

The given percentage $25\% $ thus, can be also represented as $\dfrac{{25}}{{100}}$.

Thus, the fraction form of the given percentage is $\dfrac{{25}}{{100}}$.

Simplify the fractional form obtained to determine the simplest form of the given percentage.

$\dfrac{{25}}{{100}} = \dfrac{1}{4}$

Hence, the simplest form is $\dfrac{1}{4}$.

Now, the decimal form of the given percentage is obtained by dividing the simplest form which is obtained above.

$\dfrac{1}{4} = 0.25$

Therefore, for $25\% $, the fractional form is $\dfrac{{25}}{{100}}$, the simplest form is $\dfrac{1}{4}$ and the decimal form is found to be $0.25$.

b) The percentage is $150\% $.

Ans: The percentage of any number $n$, that is $n\% $, is written as $\dfrac{n}{{100}}$.

The given percentage $150\% $ thus, can be also represented as $\dfrac{{150}}{{100}}$.

Thus, the fraction form of the given percentage is $\dfrac{{150}}{{100}}$.

Simplify the fractional form obtained to determine the simplest form of the given percentage.

$\dfrac{{150}}{{100}} = \dfrac{3}{2}$

Hence, the simplest form is $\dfrac{3}{2}$.

Now, the decimal form of the given percentage is obtained by dividing the simplest form which is obtained above.

$\dfrac{3}{2} = 1.5$

Therefore, for $150\% $, the fractional form is $\dfrac{{150}}{{100}}$, the simplest form is $\dfrac{3}{2}$ and the decimal form is found to be $1.5$.

c) The percentage is $20\% $.

Ans: The percentage of any number $n$, that is $n\% $, is written as $\dfrac{n}{{100}}$.

The given percentage $20\% $ thus, can be also represented as $\dfrac{{20}}{{100}}$.

Thus, the fraction form of the given percentage is $\dfrac{{20}}{{100}}$.

Simplify the fractional form obtained to determine the simplest form of the given percentage.

$\dfrac{{20}}{{100}} = \dfrac{1}{5}$

Hence, the simplest form is $\dfrac{1}{5}$.

Now, the decimal form of the given percentage is obtained by dividing the simplest form which is obtained above.

$\dfrac{1}{5} = 0.2$

Therefore, for $20\% $, the fractional form is $\dfrac{{20}}{{100}}$, the simplest form is $\dfrac{1}{5}$ and the decimal form is found to be $0.2$.

d) The percentage is $5\% $.

Ans: The percentage of any number $n$, that is $n\% $, is written as $\dfrac{n}{{100}}$.

The given percentage $5\% $ thus, can be also represented as $\dfrac{5}{{100}}$.

Thus, the fraction form of the given percentage is $\dfrac{5}{{100}}$.

Simplify the fractional form obtained to determine the simplest form of the given percentage.

$\dfrac{5}{{100}} = \dfrac{1}{{20}}$

Hence, the simplest form is $\dfrac{1}{{20}}$.

$\dfrac{1}{{20}} = 0.05$

Therefore, for $5\% $, the fractional form is $\dfrac{5}{{100}}$, the simplest form is $\dfrac{1}{{20}}$ and the decimal form is found to be $0.05$.

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

Ans: The percentage of females is given as $30\% $ and the percentage of males in a city is $40\% $.

Therefore, the total percentage of males and females in a city is the addition of both the percentages given.

${\text{The total percentage of males and females in a city}}$ = 30% + 40%

${\text{The total percentage of males and females in a city}} = 70\% $

The total percentage of the children in the city will be the difference of total percentage of population in the city and the total percentage of males and females in the city.

${\text{The percentage of children in the city}} = {\text{Total percentage }} - {\text{Percentage of males and females}}$${\text{The percentage of children in the city}} = 100\% - 70\% $

Thus,

${\text{The percentage of children in the city}} = 30\% $

Hence, the percentage of children in the city is found to be $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?

Ans: The total number of voters in a constituency is given to be $60\% $.

Of the given number of voters $60\% $ candidates voted.

The percentage of the candidates that did not vote will be the difference of the total percentage of the candidates and the percentage of candidates that voted.

${\text{The percentage of candidates that did not vote}}$ = 100% - 60%

${\text{The percentage of candidates that did not vote}} = 40\% $

Now, the actual number of candidates who did not vote is calculated as $40\% $ of the total number of voters in the constituency, that is, $40\% $ of 15000.

${\text{The number of candidates who did not vote}} = \dfrac{{40}}{{100}} \times 15000$

${\text{The number of candidates who did not vote}} = 6000$

Therefore, the number of candidates who did not vote is 6000.

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

Ans: Assume Meeta’s total salary to be ₹$x$.

It is given that she saves ₹ 4000 from her salary which is $10\% $ of her total salary.

This can be represented as follows,

$10\% {\text{ of total salary}} = 4000{\text{ Rs}}$

The percentage of any number $n$, that is $n\% $, is written as $\dfrac{n}{{100}}$.

Thus,

$10\% {\text{ of }}x = 4000{\text{ }}$

$\dfrac{{10}}{{100}} \times x = 4000$

On evaluation further and cross- multiplying,

$x = \dfrac{{4000 \times 100}}{{10}}$

$x = 40000$

Therefore, Meeta’s total salary is found to be ₹40000.

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

Ans: It is given that in one season the local cricket team played 20 matches out of which they won $25\% $ matches.

Thus, the total number of matches won by them will be $25\% $ of the number of matches played by them which is represented as follows,

${\text{Total matches won by the team}} = 25\% {\text{ of }}20$

Now, the percentage of any number $n$, that is $n\% $, is written as $\dfrac{n}{{100}}$.

Thus,

${\text{Total matches won by the team}} = \dfrac{{25}}{{100}} \times {\text{ }}20$

${\text{Total matches won by the team}} = \dfrac{1}{4} \times {\text{ }}20$

${\text{Total matches won by the team}} = 5$

Therefore, the number of matches that the team won is found to be 5.

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

Opting for the NCERT solutions for Ex 8.2 Class 7 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 8.2 Class 7 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

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