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

## 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 \(600\)

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

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