Ex.13.2 Q9 Direct and Inverse Proportions Solution - NCERT Maths Class 8

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Question

A car takes \(2\) hours to reach a destination by travelling at a speed of \(60\,\rm{ km/hour.}\) How long will it take when the car travels at a speed of \(80\,\rm{km/hour}?\)

Text Solution

What is Known?

\(2\) hours to reach at a speed of \(60\,\rm{km/hour.}\)

What is Unknown?

If the speed is \(80\,\rm{km/hour},\) the number of hours to reach.

Reasoning:

Two numbers \(x\) and \(y\) are said to vary in inverse proportion if

\[\begin{align}xy = {\rm{ }}k,{\rm{ }}x{\rm{ }} = {\rm{ }}\frac{1}{y}k\end{align}\]

Where \(k\) is a constant.

\[\begin{align}{x_1}{y_1} = {x_2}{y_2}\end{align}\]

Steps:

If the speed increases, the time required to reach will decrease. Hence, it is inverse proportion.

\[\begin{align}{x_1}{y_1} &= {x_2}{y_2}\\60 \times 2 &= 80 \times {y_2}\\{y_2} &= \frac{{60 \times 2}}{{80}}\\{y_2} &= \frac{3}{2}\\{y_2} &= 1\frac{1}{2}\;{\rm{hours}}\end{align}\]

Hence \(\begin{align}1\frac{1}{2}\end{align}\) hours are required to reach the destination if the speed is increased to \(80\,\rm{km/hour.}\)