Question

The sum of the ages of $A$ and $B$ is $85$ years. $5$ years ago, the age of $A$ was twice that of $B$. Find the present ages

Answer 1

Let the present age of $A$ be $x$ years and that of $B$ be $y$ years.

Then $x+y=85$. Five years back, age of $A$ was $x-5$ and that of $B$ was $y-5$.

Hence $x-5=2(y-5)$. Thus we have

$x+y=85,\left(1\right)$

$-x+2y=5.\left(2\right)$

Adding both the equations, we get $3y=90$ and hence $y=30$. This implies $x=85-y=85-30=55$.

Thus the present age of $A$ is $55$ years and that of $B$ is $30$ years.