# Exercise 8.2 Comparing-Quantities -NCERT Solutions Class 7

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## Chapter 8 Ex.8.2 Question 1

Convert the given fractional numbers to percent.

(a) \begin{align}\frac{1}{8}\end{align}

(b) \begin{align}\frac{5}{4}\end{align}

(c) \begin{align}\frac{3}{{40}}\end{align}

(d) \begin{align}\frac{2}{7}\end{align}

### Solution

What is Known?

Fractional numbers.

What is Unknown?

Conversion of Fractional numbers into percentage.

Reasoning:

To convert fraction into percentage we will have to multiply the fraction by $$100$$ because $$1\%$$ means $$1$$ part of $$100$$ i.e. $$1/100.$$

Steps:

\begin {align}{\rm{(a)}}\quad\,\frac{1}{8} &= \frac{1}{8} \times 100 \% \\&= 12.5\% \end{align}

\begin {align}{\rm{(b)}}\quad\frac{5}{4} &= \frac{5}{4} \times 100\% \\&= 125 \% \end{align}

\begin {align}{\rm{(c)}}\quad\frac{3}{{40}} &= \frac{3}{{40}} \times 100\% \\&= 7.5 \% \end{align}

\begin {align}{\rm{(d)}}\quad\frac{2}{7} &= \frac{2}{7} \times 100\% \\&= 28\frac{4}{7} \% \end{align}

## Chapter 8 Ex.8.2 Question 2

Convert the given decimal fractions to per cents.

a) $$0.065$$

(b) $$2.1$$

(c) $$0.02$$

(d) $$12.35$$

### Solution

What is Known?

Numbers in the decimal form.

What is Unknown?

Per cent form of the given numbers.

Reasoning:

First convert the decimal form into fractions and after that multiply the fraction with $$100$$ to convert it into percentage.

Steps:

(a) \begin{align}&0.65 = \frac{{65}}{{100}}\\ &\frac{{65}}{{100}} \times 100 = 65\%\end{align}

(b) \begin{align}&2.1 = \frac{{21}}{{10}}\\ &\frac{{21}}{{10}} \times 100 = 210\%\end{align}

(c) \begin{align}&0.02 = \frac{2}{{100}}\\ &\frac{2}{{100}} \times 100 = 2\%\end{align}

(d) \begin{align}&12.35 = \frac{{1235}}{{100}}\\ &\frac{{1235}}{{100}} \times 100 = 1235 \%\end{align}

## Chapter 8 Ex.8.2 Question 3

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

### Solution

What is Known?

The part of the figures which is coloured .

What is Unknown?

What part of the figures is coloured and also the per cent which is coloured.

Reasoning:

In this question first find the the total number of parts of the figure and then the coloured parts. The fraction of coloured part is obtained by dividing number of coloured part with total umber of parts.To find the percentage multiply the given fraction by $$100.$$

Steps:

(i) In this figure, one part out of four parts is coloured. So the fraction of coloured part is \begin{align}\frac{1}{4}\end{align}. Convert the fraction into percentage by multiplying the fraction with $$100.$$

Percentage of coloured part

\begin{align}&= \frac{1}{4} \times 100 \\& = 25\% \\\end{align}

(ii) In this figure, three parts out of five parts are coloured. Hence the fraction of coloured parts is \begin{align}\frac{3}{5}\end{align}

Percentage of coloured part

\begin{align}&= \,\frac{3}{5} \times 100\\&= 60\%\end{align}

(iii) In this figure, three parts out of eight parts are coloured. Hence the fraction of coloured parts is\begin{align}\frac{3}{8}\end{align}

Percentage of coloured part

\begin{align}&= \frac{3}{8} \times 100\\&= 37.5\%\end{align}

## Chapter 8 Ex.8.2 Question 4

Find:

(a) $$15\%\, {\rm{ of }}\,250$$

(b) $$1\% \,{\rm{ of\, }}1\,{\rm{ hour }}$$

(c) $$20\% \,{\rm{ of \,Rs\, }}2500$$

(d) $$75\%\, {\rm{ of \,}}1{\rm{kg}}$$

### Solution

What is Known?

Some quantities (numbers).

What is Unknown?

The per cent of the given quantities (numbers).

Reasoning:

First convert the given percentage into fraction by dividing it by $$100$$ then multiply it with the given quantity (number) to get the answer.

Steps:

(a) \begin{align}15\% {\text{ of }}250\\ 15\% &= \frac{{15}}{{100}}\\ 15\% {\text{ of }}250 \, &= \frac{{15}}{{100}} \times 250\\ &= 37.5\%\end{align}

(b) \begin{align}1\% {\text{ of }}1{\rm{ hour }}\\ 1\% &= \frac{1}{{100}}\\1\% {\rm{ of }}1{\text{ hour }} &= \frac{1}{{100}} \times 60{\text{min}}\\ &= 0.6{\rm{ minutes }}\end{align}

(c)  \begin{align}20\% {\text{ of Rs }}2500\\ 20\% \, &= \frac{{20}}{{100}}\\\,\,\,\,\,\,20\% {\text{ of Rs }}2500\, &= \frac{{20}}{{100}} \times 2500\\ &= {\text{Rs}}\,500\end{align}

(d)  \begin{align}75\% {\text{ of }}1{\text{kg}}\\75\% &= \frac{{75}}{{100}}\\75 \% {\text{ of }}1{\text{kg}} &= \frac{{75}}{{100}}{\rm{x}}1000{\text{gms}}\\& = 750{\text{gms}}\end{align}

## Chapter 8 Ex.8.2 Question 5

Find the whole quantity if

(a) $$5\%$$ of it is $$600.$$

(b) $$12\%$$ of it is $$\rm Rs\, 1080.$$

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

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

(e) $$8\%$$of it is $$40$$ litres.

### Solution

What is Known?

Percentage of a quantity.

What is Unknown?

The whole quantity.

Reasoning:

First convert the percentage into fraction and assume the total quantity as $$A.$$

Steps:

(a) $$5\%$$ of it is $$600.$$

Assume whole quantity to be $$A.$$ \begin{align}5\%=\frac{5}{100}.\end{align} Since, $$5\%$$ of it is $$600$$

So,

$\frac{5}{{100}} \times A = 600$

Or

\begin{align} A &= 600 \times \frac{{100}}{5}\\ &= 12000\end{align}

(b) $$12\%$$ of it is $$\rm Rs\,1080.$$

Assume total amount to be $$A.$$ Since, $$12%$$ of A is $$\rm Rs\, 1080.$$

So,

$\frac{{12}}{{100}} \times A = 1080$

Or

\begin{align}A &= 1080 \times \frac{{100}}{{12}}\\&= 9000\end{align}

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

Assume total distance to be $$A.$$ Since, $$40\%$$ of $$A$$ is $$500 \,\rm km.$$

So,

$\frac{{40}}{{100}}\, \times A = 500$

Or

\begin{align} A &= 500 \times \frac{{100}}{{40}}\\ &= 1250\,{\rm{km}}\end{align}

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

Assume total time to be $$A.$$ Since, $$70\%$$ of it is $$14$$ minutes.

So,

$\frac{{70}}{{100}}\, \times A = 14$

Or

\begin{align} A &=14 \times \,\,\frac{{100}}{{70}}\\&= 20\,{\rm{minutes}}\end{align}

(e) $$8\%$$ of it is $$40$$ litres.

Assume total amount to be $$A.$$ Since, $$8\%$$ of $$A$$ is $$40$$ litres

So,

$\frac{8}{{100}} \times A = 4$

Or

\begin{align} A &= 40\,\, \times \frac{{100}}{8}\\&= 500\,{\rm{litres}}\end{align}

## Chapter 8 Ex.8.2 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

What is Known?

Percentages.

What is Unknown?

Decimal fractions and fractions in simplest forms of given percentages.

Reasoning:

To convert given percentage into decimal fractions, divide it by $$100$$ and to convert the fraction to its simplest form, divide both the numerator and denominator by the common factor. Repeat this process until there are no more common factors. The fraction thus obtained is the simplest form of the fraction.

Steps:

(a) $$25\%$$

So, decimal fraction will be

\begin{align}& = \frac{{25}}{{100}}\\& = 0.25\end{align}

& Simplest form of fraction will be

\begin{align}\frac{{25}}{{100}} & = \frac{5}{{20}}\\ & = \frac{1}{4}\end{align}

(b) $$150\%$$

So, decimal fraction will be

\begin{align}& = \frac{{150}}{{100}}\\&={1.50}\end{align}

& Simplest form of fraction will be

\begin{align}\frac{{150}}{{100}} & = \frac{{30}}{{20}}\\& = \frac{3}{2}\end{align}

(c) $$20\%$$

So decimal fraction will be

\begin{align}& = \frac{{20}}{{100}}\\& = 0.20\end{align}

& Simplest form of fraction will be

\begin{align}\frac{{20}}{{100}} & = \frac{2}{{10}}\\ & = \frac{1}{5}\end{align}

(d) $$5\%$$

So decimal fraction will be

\begin{align}& = \frac{5}{{100}}\\& = 0.05\%\end{align}

& Simplest form of fraction will be

\begin{align}\frac{5}{{100}} & = \frac{1}{{20}}\end{align}

## Chapter 8 Ex.8.2 Question 7

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

### Solution

What is Known?

In a city, $$30\%$$ are females, $$40\%$$ are males and remaining are children.

What is Unknown?

Percentage of children.

Reasoning:

Consider the total percentage as $$100\%$$. Since, percentage of males and females is known, percentage of children can be obtained by subtraction total percentage of males and females from $$100\%$$.

Steps:

Total percentage is equal to $$100\%$$. out of $$100\% , 30\%,$$ are females, $$40 \%$$ are females and the remaining are children.

So, the percentage of children

\begin{align}&= 100\% - 30\% - 40\% \\&= 30\% \end{align}

## Chapter 8 Ex.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?

### Solution

What is Known?

Out of total voters $$(15,000)$$ in a constituency, the percentage of voter $$(60\%)$$ that voted

What is Unknown?

The percentage of voters who did not vote and number of voters that did not vote.

Reasoning:

Consider total percentage of voters as $$100\%.$$ Since the percentage of voters that voted is given, percentage of voters that did not vote can be obtained. The percentage can be used to obtain the number of voters that did not vote.

Steps:

Total percentage of voters is equal to $$100\%.$$ Percentage of voters that voted is given to be $$60\%.$$

So, the percentage of voters who did not vote will be

$$(100\% - 60\%) = 40\%$$

The number of voters who did not vote

\begin{align}&={\rm{ 40\% \,of \,15,000 }}\\&=\frac{{{\rm{40}}}}{{{\rm{100}}}} \times {\rm{15,000}}\\ &=\rm{ 6,000}\end{align}

## Chapter 8 Ex.8.2 Question 9

Meeta saves $$\rm Rs \,400$$ from her salary. If this is $$10 \%$$ of her salary. What is her salary?

### Solution

What is Known?

The amont of money that Meet saved from her salary and the percentage of her salary the saving is equal to.

What is Unknown?

Salary of Meeta.

Reasoning:

Assume the salary to be $$A.$$ Since $$10 \%$$ of $$A$$ is known, $$100 \%$$ of $$A$$ (total salary) of Meeta can be obtained.

Steps:

Let the total salary be Rs $$A.$$ If $$10 \%$$ of$$A$$ is $$400$$

Thus,

\begin{align} \frac{{10}}{{100}} \times A = 400\end{align}

Or

\begin{align} A = 400 \times \frac{{100}}{{10}}\\= 4000 \end{align}

Thus, the total salary is $$\rm Rs. 4000$$

## Chapter 8 Ex.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?

### Solution

What is Known?

Matches played by a cricket team in a season and percentages of matches won.

What is Unknown?

Number of matches won by the tean.

Reasoning:

Matches won by local cricket team is $$25\%$$ of $$20.$$

Steps:

Matches won

\begin{align}&={\text{ 25% }}\,{\text{of}}\,{\text{20}}\\&= \frac{{25}}{{100}} \times 20\\&= 5\end{align}

So, the matches won are $$5.$$

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