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. Find the present age of Rahul.

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)
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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)
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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.
[1 mark]


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.