The age of the father is three times as old as his son. After the twelve years, the age of the father is twice as that of his son. Find their present ages.
The age of the father is three times as old as his son. After the twelve years, the age of the father is twice as that of his son. Find their present ages.

Let’s assume the present ages of the father as a years and that of his son’s age as b years.

From the question it’s given that,

Father is 3 times as old as his son. (Present)

So, the equation formed is

a=3b

⇒ a-3b=0……. (I)

Now from the given question is,

After 12 years, father’s age will be (a+12) years and son’s age will be (b+12) years.

so, the relation between their ages after 12 years is given below

a+12=2(b+12)

a+12=2b+24

⇒ a-2b-12=0…… (ii)

Solving (i) and (ii), we get the solution

By using cross-multiplication, we have

a-3-12-(-2)0 =-b1-12-10=11-2-1(-3)

a36-0=-b-12-0 1-2+3

a36=-b-12=11

a36=b12= 1

a=36, b=12

So, the present age of father is 36 years and the present age of son is 12 years.