Question

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

Answer 1

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

In a map $\frac{1}{4}cm$ represents $25km$

$\therefore$ We need to find how much does $\frac{5}{2}$ represent.

Let the distance to be found out be $x$

$\therefore \frac{1}{4}:\frac{5}{2}::25:x$

$\Rightarrow \frac{\frac{1}{4}}{\frac{5}{2}}=\frac{25}{x}$

On simplifying,

$\Rightarrow \frac{1\times 2}{4\times 5}=\frac{25}{x}$

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

$\Rightarrow \frac{1}{10}=\frac{25}{x}$

On cross multiplying,

$\Rightarrow x=10\times 25$

$\Rightarrow x=250km$