Question

The ages of $A$ and $B$ are in the ratio $5:6$. Five years from now Their ages will be $6:7$. Find their present ages.

Answer 1

Let A present age is a.

Let B present age is b.

For,

$a:b$ $=$ $5:6$

Let the common multiple be c. there fore,

$a=5c$ and $b=6c$ and

A age fine years from now is $a+5$

B age fine years from now is $b+5$

hence,

$\left(a+5\right):\left(b+5\right)=6:7$

$\Rightarrow$ $\frac{5c+5}{6c+5}=\frac{6}{7}$

$\Rightarrow$ $35c+35=36c+30$

hence the $c=5$

hence the present age of A is $25$

and B is $30$