Percentages Question 2 - CAT 2021
The total of the male and female populations in a city increased by 25% from 1970 to 1980.
During the same period:
- Male population increased by 40%.
- Female population increased by 20%.
From 1980 to 1990, the female population increased by 25%.
If in 1990, the female population was twice the male population, then the percentage increase in the total population from 1970 to 1990 was:
Step-by-Step Explanation
Assume that in 1990:
- Male population = 100
- Female population = 200
Since the female population increased by 25% from 1980 to 1990,
Female population in 1980:
200 / 1.25 = 160
Since the female population increased by 20% from 1970 to 1980,
Female population in 1970:
160 / 1.2 = 400 / 3
Let the male population in 1970 be x.
Using the fact that the total population increased by 25% from 1970 to 1980,
1.25 × (x + 400 / 3) = 1.4x + 160
Solving,
x = 400 / 9
The percentage increase from 1970 to 1990 comes out to
68.75%
Hence, the correct answer is Option B.
💡 FundaMakers Tip: In population questions, assume convenient values for the final population and work backwards using the given percentage changes.