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.