Question

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

Answer 1

The scale of the map = 1 : 4000000.
This means that 1 unit of distance on the map is equal to 4000000 units of the actual distance.
So, let us assume that the actual distance between the towns = 'x' cm.
Now, it is given that
1 : 4000000 = 5 : x
Hence, 1, 4000000, 5 and x are in proportion.
Therefore, product of extremes = product of means
= $1\times x=5\times 4000000$
= x = $\frac{5\times 4000000}{1}$ = 20000000 cm
Since 1 km = 1000 m =1000$\times$1 m =1000$\times$100 cm = 100000 cm (1 m =100 cm),
x = $\frac{20000000}{100000}$ = 200 km