Question

The ages of $A$ and $B$ are in the ratio $3:5$. Eight years hence, their ages will be in the ratio $5:7$ Find their present ages.

Answer 1

Let the present ages of $A$ and $B$ be $3x$ and $5x$ respectively.

According to the question-

$\frac{3x+8}{5x+8}=\frac{5}{7}$

$7(3x+8)=5(5x+8)$

$21x+56=25x+40$

$25x-21x=56-40$

$\Rightarrow x=\frac{16}{4}=4$

Therefore,

Present age of $A=3\times 4=12$ years

Present age of $B=5\times 4=20$ years