Question

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.

Answer 1

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

$\therefore x+y=5000--------\left(1\right)$

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

$\therefore$The number of males after a year will be$=x+\frac{5x}{100}=\frac{105x}{100}$

$\therefore$The number of females after a year will be$=y+\frac{3y}{100}=\frac{103y}{100}$

Also, given that

$\frac{105x}{100}+\frac{103y}{100}=5202⟹105x+103y=520200--------\left(2\right)$

Equation (1)$\times 105⟶105x+105y=525000$

Equation (2)$\times 1⟶105x+103y=520200$

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

$\Rightarrow 2y=4800\Rightarrow y=2400$ then substitute in $\left(1\right)$ we get $x=5000-y\Rightarrow x=5000-2400=2600$

$\therefore y=2400$

$\therefore x=2600$