# Ex.13.1 Q10 Direct and Inverse Proportions Solution - NCERT Maths Class 8

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## Question

A loaded truck travels $$14\,\rm{km}$$ in $$25$$ minutes. If the speed remains the same, how far it travels in $$5$$ hours?

## Text Solution

What is Known?

Truck travels $$14\,\rm{km}$$ in $$25$$ minutes.

What is Unknown?

Distance travelled in $$5$$ hours.

Reasoning:

Two numbers $$x$$ and $$y$$ are said in direct proportion if,

\begin{align}\frac{x}{y} = k,\quad x = k\,y\end{align}

Where $$k$$ is a constant.

Steps:

In $$25$$ minutes, it travels $$14 \,\rm{km}$$. In $$5$$ hours, it will travel more distance. So, it is a case of direct proportion.

 ${{\bf{Distance}}}$ ${{\bf{Time\; in \; minutes}}}$ $${{\rm{14}}}$$ $${{\rm{25}}}$$ $${\,{\rm{?}}}$$ $${{\rm{5 \times 60 }}\left( {{\rm{1 hour = 60 \rm{minutes}}}} \right)}$$

[For comparison the unit should be same]

\begin{align}\frac{{{x_1}}}{{{y_1}}} &= \frac{{{x_2}}}{{{y_2}}}\\\frac{{14}}{{25}} &= \frac{{{x_2}}}{{5 \times 60}}\\25\,{x_2} &= 5 \times 60 \times 14\\{x_2} &= \frac{{5 \times 60 \times 14}}{{25}}\\{x_2} &= 168\;{\rm{km}}\end{align}

Hence the truck can travel $$168 \,\rm{km}$$ in $$5$$ hours.

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