Question

In England the population increased $15.9$ per cent, between $1871$ and $1881$; if the town population increased $18$ per cent, and the country population $4$ per cent, compare the town and country populations is $1871$.

Answer 1

Let $x$ be the town population, $y$ be the country population then $x+y$ wiil be the total population, then

Increase in town population=$\frac{18x}{100}$

Increase in country population=$\frac{4y}{100}$

Increase in total population$\frac{15.9}{100}(x+y)$

Then,

$\frac{18x}{100}+\frac{4y}{100}=\frac{15.9}{100}(x+y)$

$18x+4y=15.9x+15.9y$

$2.1x=11.9y$

$\frac{x}{y}=\frac{11.9}{2.1}=\frac{17}{3}$