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CAT 2021 Slot 3 — QA Question 19

Successive Percentage ChangeEasy

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

Answer & solution

  • A

    68.50

  • B

    69.25

  • 68.75

  • D

    68.25

Solution

Easy

Let males =m=m, females =f=f in 1970. The 1970 ⁣→ ⁣19801970\!\to\!1980 growth facts (40%40\% male, 20%20\% female, 25%25\% total) fix the ratio m:fm:f. Then apply the 1980 ⁣→ ⁣19901980\!\to\!1990 female growth and the "female == twice male in 1990" condition, and compare the 1990 total to 1970.

1

Fix the 1970 ratio. Total grows 25%25\%, so 1.4m+1.2f=1.25(m+f)1.4m + 1.2f = 1.25(m+f).

1.4m+1.2f=1.25m+1.25f⇒ 0.15m=0.05f⇒ f=3m\begin{aligned} &1.4m + 1.2f = 1.25m + 1.25f\\ &\Rightarrow\ 0.15m = 0.05f\\ &\Rightarrow\ f = 3m \end{aligned}
2

1980 figures. Take f=3mf=3m, total 1970=4m1970 = 4m.

Males80=1.4mFemales80=1.2⋅3m=3.6m\begin{aligned} &\text{Males}_{80} = 1.4m\\ &\text{Females}_{80} = 1.2\cdot 3m = 3.6m \end{aligned}
3

1990 figures. Females grow 25%25\%; females are twice males.

Females90=1.25⋅3.6m=4.5m⇒ Males90=12⋅4.5m=2.25m(female=2×male)⇒ Total90=4.5m+2.25m=6.75m\begin{aligned} &\text{Females}_{90} = 1.25\cdot 3.6m = 4.5m\\ &\Rightarrow\ \text{Males}_{90} = \tfrac12\cdot 4.5m = 2.25m\quad\text{(female}=2\times\text{male)}\\ &\Rightarrow\ \text{Total}_{90} = 4.5m + 2.25m = 6.75m \end{aligned}
4

Percentage increase 1970→19901970\to1990. From 4m4m to 6.75m6.75m.

6.75m−4m4m×100=2.754×100⇒ =68.75%\begin{aligned} &\frac{6.75m - 4m}{4m}\times 100 = \frac{2.75}{4}\times 100\\ &\Rightarrow\ = 68.75\% \end{aligned}
68.75%68.75\%
CAT 2021 Slot 3 QA Q19: The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, — Solution | TheCATExam