Question

Present ages of Mohan and Gopal are in the ratio of $4:5$. Eight years from now the ratio of their ages will be $5:6$. Find their present ages.

Answer 1

Let the present ages of Mohan and Gopal be $x$ and $y$ respectively ,

$\therefore \frac{x}{y}=\frac{4}{5}\Rightarrow 5x-4y=0⟶\left(i\right)\times 5$

After $8$ years , there ages will be $(x+8)$ years and $(y+8)$ years

$\therefore$ According to question

$\frac{x+8}{y+8}=\frac{5}{6}\Rightarrow 6x+48=5y+406x-5y=-8⟶\left(ii\right)\times 425x-20y=024x-20y=-32$

On substracting : $x=32$ years

putting $x$ in $⟶\left(i\right),$

$4y=5\times 32$

$\therefore y=40$ years.