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# The population of the village is 5000. If in a year, the numbers of males were to increase by 5% and that of the female by 3% annually the population would grow to 5202 at the end of the year. Find the number of males and females in the village.

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Solution

## 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+5x100=105x100∴The number of females after a year will be=y+3y100=103y100Also, given that105x100+103y100=5202⟹105x+103y=520200−−−−−−−−(2)Equation (1)×105⟶105x+105y=525000Equation (2)×1⟶105x+103y=520200On 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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