Averages , Ratio and Proportion Question 4 - CAT 2021
The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from 1970 to 1990 is:
Step-by-Step Explanation
- Analyze the 1970 to 1980 timeline using alligation:
From 1970 to 1980, the male population grew by 40%, the female population grew by 20%, and the total population grew by 25%.
Male 1970/Female 1970 = (25 − 20)/(40 − 25) = 5/15 = 1/3
Let us choose convenient starting values for 1970:
Male 1970 = 100
Female 1970 = 300
Total 1970 = 400
- Calculate the absolute populations for 1980:
Male 1980 = 100 × 1.40 = 140
Female 1980 = 300 × 1.20 = 360
- Calculate the absolute populations for 1990:
The female population increases by 25% from 1980 to 1990:
Female 1990 = 360 × 1.25 = 450
In 1990, the female population is exactly twice the male population:
Male 1990 = 450/2 = 225
Total 1990 = 450 + 225 = 675
- Find the overall net percentage increase from 1970 to 1990:
Percentage Increase = ((675 − 400)/400) × 100% = (275/400) × 100% = 68.75%
Correct Option: B
💡 FundaMakers Tip:
Using alligation on the first population growth phase establishes a reliable base ratio (Male : Female = 1 : 3) immediately. Choosing standard numbers like 100 and 300 based on this ratio avoids messy fractional variables later on.