# A father is three times as old as his son. In 12 years time, he will be twice as old as his son. Find the present ages of father and the son.

Given :

A father is three times as old as his son. In 12 years time, he will be twice as old as his son.

To find :

We have to find the present ages of the father and the son.

Solution :

Let the present age of the son be $x$.

This implies,

The age of the father $= 3x$

Age of the son after 12 years $= x+12$

Age of the father after 12 years $= 3x+12$.

After twelve years, the father's age will be twice as that of his son.

Therefore,

$3x+12 = 2(x+12)$

$3x+12 = 2x+24$

$3x-2x = 24-12$

$x = 12$

$\Rightarrow 3x=3(12)=36$ years

The present age of the son is $12$ years and the present age of the father is $36$ years.

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