Question

The population of a certain town was $50,000$. In year, the male population increased by $5\%$ and the female population increased by $8\%$. Now the population becomes $53,220$. What was the number of male and female in the previous year.

Answer 1

Male population $=x$

Female population$=y$

$x+y=50,000$

$y=50,000-x$

$x$ increased $5\%$

$y$ increased $8\%$

$(x+x\times 5\%)+(y+y\times 8\%)=53220$

$x+\frac{5x}{100}+y+\frac{8y}{100}=53220$

$100x+5x+100y+8y=5322000$

as $y=50,000-x$

$100x+5x+108(50,000-x)=5322000$

$105x-108x+5400000=5322000$

$5400000-5322000=3x$

$78000=3x$

$x=26000$

$y=50,000-x=50,000-26000$

$y=24000$

$\therefore$ Male population$=26000$

Female population$=24000$