Let’s assume the present ages of the father as x years and that of his son’s age as y years.
From the question it’s given that,
After 10 years, father’s age will be (x+10) years and son’s age will be (y + 10) years.
So, the equation formed is
x + 10 = 2(y + 10)
x – 10 = 2y + 20
x – 2y – 10 = 0……… (i)
Also again from the question it’s given as,
Before 10 years, the age of father was (x – 10) years and the age of son was (y – 10) years.
Furthermore, the relation between their 10 years ago is given below
x – 10 = 12(y – 10)
x – 10 = 12y – 120
x – 12y + 110 = 0……… (ii)
Thus, by solving (i) and (ii), we get the required solution
Using cross-multiplication, we have
⇒ x = 34, y = 12
Hence, the present age of father is 34 years and the present age of the son is 12 years.