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 $$4 \,\rm{cm}$$.

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