# 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.

## 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 $$600$$

${\text{So}}, \frac{5}{{100}} \times {\text{A}} = 600$

\begin{align}{\text{Or}} \, {\text{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 $$\rm Rs\, 1080.$$

${\rm{So,}}\, \frac{{12}}{{100}} \times {\rm{A}} = 1080$

\begin{align}{\rm{Or}} \, {\rm{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 $$500 \,\rm km.$$

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

\begin{align}{\rm{Or}}\,{\rm{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.

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

\begin{align}{\rm{Or}} \, {\rm{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

${\rm{So}}, \frac{8}{{100}}\, \times \,{\rm{A}} = 4$

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

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