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

- 68.75
- 68.50
- 68.25
- 69.25

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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%

Choice A is the correct answer.

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