Question

Today Sanjay is $20$ years younger than his father. Ten years ago he was one-half as old as his father. How old will his father be $10$ years hence ?

• A. $40$ years
• B. $60$ years
• C. $50$ years
• D. $30$ years

Answer 1

The correct option is B $60$ years

Let the present ages of Sanjay and his father be $x$ and $y$ respectively.
Today Sanjay is 20 years younger than his father.
$\therefore$ $x=y-20$
$\therefore$ $x-y=-20$ ...(1)
Ten years ago he was one-half as old as his father.
$\therefore$ $x-10=\frac{y-10}{2}$

$\therefore$ $2x-y=10$ ...(2)
Solving (1) and (2) we get,
$x=30$ and $y=50$
Age of father 10yrs hence will be $50+10=60$ years