Question

The scale of a map is 1:20000000. On the map, the distance between Cairo and Addis Ababa is 12 cm.
(i) Calculate the distance in kilometres between Cairo and Addis Ababa?

Answer 1

Hint: We start solving the problem by finding the relation between 1 cm on a map with total number of kilometres in real using the conversion 1 cm = ${10}^{-5}km$. We then use this result to find the distance between Cairo and Addis Ababa by multiplying 12 cm with the obtained relation. We then make the necessary calculations to get the required value of distance in kilometres.

Complete step-by-step answer:
According to the problem, we are given that the scale of a map is 1:20000000 and the distance between is given as 12 cm on the map. We need to find the distance in kilometres between Cairo and Addis and Ababa.
We know that 1:20000000 means that 1 cm on the map is equal to 20000000cm.
We know that 1 cm = ${10}^{-5}km$. So, 1 cm on the map is equal to $20000000\times {10}^{-5}=200km$. So, the representative fraction is defined as 1 cm on map = 200 km in real ---(1).
Now, we are given that the distance between Cairo and Addis Ababa is 12 cm on the map.
Let us use the result obtained in equation (1) to find the distance between Cairo and Addis Ababa in real.
So, the distance between Cairo and Addis Ababa in real = $12\times 200=2400km$.
∴ The distance between Cairo and Addis Ababa is 2400 kilometres.

Note: Whenever we get this type of problem, we first find the relation between the distance on the map and distance on the real. We should not confuse conversion while solving this problem. We can also find the distance between Cairo and Addis Ababa in m by using the conversion that $1cm={10}^{-2}m$. Similarly, we can expect problems to find the distance between Cairo and Addis Ababa in Miles.