CAT 2021 Slot 3 · Quant · Question 10

Let the 1970 populations be M male and F female.

The 1980 total can be written two ways: 1.4M+1.2F=1.25\left( M+F \right). So 0.15M=0.05F, giving F=3M.

Take M=1, so F=3 and the 1970 total is 4.

In 1980 the female population is 1.2\times 3=3.6, and in 1990 it is 1.25\times 3.6=4.5.

In 1990 the female population is twice the male, so the male population is 2.25 and the total is 4.5+2.25=6.75.

The increase from 1970 is \frac{6.75-4}{4}=\frac{2.75}{4}=0.6875, that is 68.75\%.

The 1980 male figure of 1.4 is never needed; it only serves to fix the ratio F=3M.