CAT 2021 Question Paper | Quant Slot 3

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 10 : 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

Video Explanation

Explanatory Answer

From 1970 to 1980,
the male population increased by 40%
the female population increased by 20%
the overall population increased by 25%

1.4M + 1.2F = 1.25(M + F)
1.4M + 1.2F = 1.25M + 1.25F
1.4M - 1.25M = 1.25F - 1.2F
0.15M = 0.05F
F = 3M
From 1980 to 1990,
Female population increased by 25%
Therefore, the female population in 1990 = 1.25 × 1.2F = 1.5F
Since, the female population in 1990 is twice the male population,
Male population in 1990 = 1.5F ÷ 2 = 0.75F
Since F = 3M,
Male population in 1990 = 2.25M
Total population in 1970 = M + F = M + 3M = 4M
Total population in 1990 = 2.25M + 1.5F = 2.25M + 4.5M = 6.75M
The percentage increase in population = \( \frac { 6.75 M - 4 M } { 4 M } \times 100 \) = \( \frac { 2.75 } { 4 } \times 100 \) = 68.75%

The answer is '68.75'

Choice A is the correct answer.

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