Question

The ages of $A$ and $B$ are in the ratio $5:7$. Eight years ago. their ages were in the ratio $7:13$. Find their present ages.

Answer 1

Let age of $A$ and $B$ be $5x$ and $7x$ respectively.

According to the question-

$\frac{5x-8}{7x-8}=\frac{7}{13}$

$13(5x-8)=7(7x-8)$

$65x-104=49x-56$

$\Rightarrow 65x-49x=104-56$

$\Rightarrow x=\frac{48}{16}=3$

Therefore,

Present age of $A=5\times 3=15$ years

Present age of $B=7\times 3=21$ years