Ex.13.1 Q8 Direct and Inverse Proportions Solution - NCERT Maths Class 8

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Question

Rashmi has a road map with a scale of \(1 \;\rm{cm}\) representing \(18 \,\rm{km}\). She drives on a road for \(72 \,\rm{km}\). What would be her distance covered in the map?

Text Solution

What is Known:

The scale of representing \(1\; \rm{cm}\) \(=\) \(18 \,\rm{km}\)

What is Unknown:

The distance covered in map when the distance on road is \(72 \,\rm{km.}\)

Reasoning:

Two numbers \(x\) and \(y\) are said in direct proportion if

\[\begin{align}\frac{x}{y} = k,\, \qquad x = y\,k\end{align}\]

Where \(k\) is a constant.

The map is a representation of very large region. The scale shows the representation of the actual length and the length represented in map.

Steps:

\(1\,\rm{cm}\) on map represents \(18 \,\rm{km}\) of actual distance then \(2\, \rm{cm}\) on the map represents \(36 \,\rm{km}\). Hence the scale is based on the concept of direct proportion.

\[\begin{align}1:18 &= x:72\\\frac{{1}}{18} &= \frac{x}{{72}}\\18 \times x &= 72 \times 1\\x &= \frac{{72}}{{18}}\\x &= 4\end{align}\]

The distance covered in the map would be \(4 \,\rm{cm}\).