Question

Six years hence, Rahul's age will be three times his son's age and three years ago, he was nine times as old as his son. Rahul's present age is:

Answer 1

Let Rahul's present age be $x$ years and his son's age be $y$ years.

Six years hence, Rahul's age = $(x+6)$ years
Son's age = $(y+6)$ years.

According to the question
$x+6=3(y+6)$
$\Rightarrow x+6=3y+18$
$\Rightarrow x-3y=12$ .....(i)

Now, three years ago, Rahul's age = $(x-3)$ years
Son's age = $y-3$ years

According to the question
$x-3=9(y-3)$
$\Rightarrow x-3=9y-27$
$\Rightarrow x-9y=-24$ ....(ii)

On subtracting (ii) from (i) we get
$6y=36\Rightarrow y=6.$

On substituting the value of $y$ in (i), we get
$x-18=12$
$\Rightarrow x=30years$

$\therefore$ Rahul's present age is 30 years.

For verification,

Presently Rahul's age is 30 years and his son's age is 6 years.
3 years back, Rahul was 27 years and son was 3 years old.
That is correct according to the given condition,
His age was 9 times more than his son's age.

6 years hence he will be 36 years and son will be 12 years old.
That is correct according to the given condition.
His age will be 3 times of his son's age.