Question

The scale of a map is $1:4000000$. What is the actual distance between two towns, if they are $5cm$ apart on the map.

Answer 1

Given that the scale of the map is $1:4000000$ .
This means that $1$ unit in the graph is equivalent to $4000000$ units in actual.

We need to find the actual distance between two cities which is $5cm$ apart in the map.

Let $x$ be the actual distance between the two cities. So, we can write it as a ratio of distance on the map to the actual distance.
$\Rightarrow 5:x$

This ratio will be proportional to the given scale of the map. So, we can write them as,

$\Rightarrow \frac{1}{4000000}=\frac{5}{x}$

On cross multiplying, we get

$\Rightarrow x=5\times 4,000,000$

On simplification, we get

$\Rightarrow x=20,000,000$

As the distance on the map is $5cm$, the unit of $x$ will be in $cm$.

$\Rightarrow x=20,000,000cm$

We know that $1cm=\frac{1}{100}m$ .

$\Rightarrow x=\frac{20,000,000}{100}m$

We also know that $1m=\frac{1}{1000}km$.

$\Rightarrow x=\frac{20,000,000}{100\times 1000}km$

$\therefore x=200km$