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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