After six year a man’s age will be three times the age of his son and three years ago, he was nine times as old as his son. Now find the present ages.
After six year a man’s age will be three times the age of his son and three years ago, he was nine times as old as his son. Now find the present ages.

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

According to question

After 6 years, the man’s age will be (a+6) years and son’s age will be (b+6) years.

So, the equation is

a+6=3(b+6)

a+6=3b+18

a-3b-12=0……. (i)

Also again from the question it’s given as,

Before 3 years, the age of the man was (a-3) years and the age of son’s was (b-3) years.

Furthermore, the relation between their 3 years ago is given below

a-3=9(b-3)

a-3=9b-27

a-9b+24=0……. (ii)

Therefore, by solving (i) and (ii), we get the  solution

Using cross-multiplication, we get

a-324-9(-12)=-b124-1(-12)=11-9-1(-3)

a-72-108=-b24+12=19+3

a-180=-b36= 1-9+3

a180=b36=16

a=1806  ,b=366

a = 30, b=6

Hence, the present age of the man is 30 bears and the present age of son is 6 bears.