Question

3. Population of a city was 6000 and next year it
increased up to 7400. If growth rate of male and
female are 20% and 30% respectively, then the
no. of females in the city was
(a) 4200 (b) 3000 (c) 4000 (d) 2000
7​

Answer 1

Answer:

Let initially the number of males and females in the population be x and y.

∴x+y=5000−−−−−−−−(1)

After a year, the number of males increases by 5% and the number of females increases by 3%.

∴The number of males after a year will be=x+

100

5x

=

100

105x

∴The number of females after a year will be=y+

100

3y

=

100

103y

Also, given that

100

105x

+

100

103y

=5202

⟹105x+103y=520200−−−−−−−−(2)

Equation (1)×105⟶105x+105y=525000

Equation (2)×1⟶105x+103y=520200

On subtracting (2) from (1), we get

⇒2y=4800⇒y=2400 then substitute in (1) we get x=5000−y⇒x=5000−2400=2600

∴y=2400

∴x=2600

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