Question:hard

The total of male and female populations in a city increased by 25% from 1970 to1980.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

Updated On: Jan 15, 2026
  • 68.75
  • 68.50
  • 68.25
  • 69.25
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The Correct Option is A

Solution and Explanation

Variables:
Initial male population (1970) = $M$
Initial female population (1970) = $F$

Population Growth (1970-1980):

  • Male population in 1980 = $1.4M$ (40% increase from 1970)
  • Female population in 1980 = $1.2F$ (20% increase from 1970)

Total population in 1980:
$1.4M + 1.2F$

Given Information:
Total population increased by 25% from 1970 to 1980.
$1.4M + 1.2F = 1.25(M + F)$

Expanding the equation:
$1.4M + 1.2F = 1.25M + 1.25F$

Rearranging to solve for the relationship between M and F:
$1.4M - 1.25M = 1.25F - 1.2F$
$0.15M = 0.05F$
$\Rightarrow \boxed{F = 3M}$

Population Growth (1980-1990):

  • Female population in 1990 = $1.25 \times (1.2F) = 1.5F$ (25% increase from 1980)
  • Given: 1990 female population is double the 1990 male population.
    $1.5F = 2 \times \text{Male}_{1990}$
    $\Rightarrow \text{Male}_{1990} = 0.75F$

Final Calculation:

Total population in 1970: $M + F = M + 3M = 4M$

Total population in 1990: $\text{Male}_{1990} + \text{Female}_{1990} = 0.75F + 1.5F = 2.25F$
Substituting $F = 3M$: $2.25 \times (3M) = 6.75M$

Percentage Increase in Total Population (1970-1990):
$\frac{6.75M - 4M}{4M} \times 100 = \frac{2.75M}{4M} \times 100 = \boxed{68.75\%}$

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