# Ex.8.2 Q5 Compairing Quantities - NCERT Maths Class 7

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## Question

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.

Video Solution
Comparing Quantities
Ex 8.2 | Question 5

## Text 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}

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