Question

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

Accepted Answer

A. Let 1970 male population be $M$ and female population be $F$. Total 1970 population = $M + F$. In 1980, male population = $1.4M$, female population = $1.2F$. Total 1980 population = $1.25(M + F)$: $$1.4M + 1.2F = 1.25M + 1.25F \implies 0.15M = 0.05F \implies F = 3M$$ Total 1970 population = $M + 3M = 4M$. 1980 population: $M_{80} = 1.4M$, $F_{80} = 3.6M$. In 1990, female population increased by 25%: $$F_{90} = 1.25 	imes 3.6M = 4.5M$$ In 1990, $F_{90} = 2 M_{90} \implies M_{90} = 2.25M$. Total 1990 population = $2.25M + 4.5M = 6.75M$. Percentage increase from 1970 to 1990: $$\frac{6.75M - 4M}{4M} 	imes 100 = \frac{2.75}{4} 	imes 100 = 68.75\%$$.

Percentage increase in male and female population

Explanation

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