# 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 $$80\,\rm{km/hour.}$$

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