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Question

In a map $$\dfrac{1}{4}$$ cm represents $$25$$ km. If two cities are $$2 \dfrac{1}{2}$$ cm apart on the map, what is the actual distance between them?


Solution

Firstly, $$2\dfrac{1}{2}=\dfrac{(2\times 2)+1}{2}=\dfrac{5}{2}\ cm$$

In a map $$\dfrac{1}{4}\ cm$$ represents $$25\ km$$
$$\therefore$$ We need to find how much does $$\dfrac{5}{2}$$ represent. 
Let the distance to be found out be $$x$$
$$\therefore \dfrac{1}{4}:\dfrac{5}{2}::25:x$$

$$\Rightarrow \dfrac{\dfrac{1}{4}}{\dfrac{5}{2}}=\dfrac{25}{x}$$
On simplifying,
$$\Rightarrow \dfrac{1\times 2}{4\times 5}=\dfrac{25}{x}$$

$$\Rightarrow \dfrac{1}{2\times 5}=\dfrac{25}{x}$$


$$\Rightarrow \dfrac{1}{10}=\dfrac{25}{x}$$
On cross multiplying,
$$\Rightarrow x=10\times 25$$
$$\Rightarrow x=250\ km$$

Mathematics

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