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

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

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