CAT 2021 Slot 3 QA Q10 Percentages & Profit-Loss

Question 10 of the Quantitative Ability (QA) section, CAT 2021 Slot 3, with CAT's official answer and a worked solution.

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
  1. A
    68.75
  2. B
    68.50
  3. C
    68.25
  4. D
    69.25

Answer: (A) 68.75 Percentages & Profit-Loss MCQ

Solution

  1. 1970: males \(M\), females \(F\). \(1.4M + 1.2F = 1.25(M + F) \Rightarrow 0.15M = 0.05F \Rightarrow F = 3M\).
  2. Take \(M = 100, F = 300\), total 400. 1980: \(M = 140\), \(F = 360\). 1990: \(F = 1.25 \times 360 = 450\), so \(M = 225\).
  3. 1990 total \(= 675\); increase \(= \frac{275}{400} = 68.75\%\).

Same concept in other years

See every question on Total change from parts growing at different percentages.

More Percentages & Profit-Loss questions from CAT

All 46 Percentages & Profit-Loss questions asked since 2017.