Question

Father’s age is three times the sum of age of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.

Answer 1

Let the present age of father be x years and the present age of his son be y years.

The present age of father is three times the age of the son. Thus, we have

`x = 3y`

`⇒ x - 3y =0`

After 12 years, father’s age will be (x + 12) years and son’s age will be (y + 12) years. Thus using the given information, we have

`x + 12 = 2(y + 12)`

`⇒ x + 12 = 2y + 24`

`⇒ x - 2y - 12 = 0`

So, we have two equations

`x - 3y = 0`

`x - 2y - 12 = 0`

Here x and y are unknowns. We have to solve the above equations for x and y.

By using cross-multiplication, we have

`x/((-3)xx(-12)-(-2)xx0)=(-y)/((1xx(-12)-1xx0))=1/((1xx(-2)-1xx(-3)))`

`⇒ x/(45-0)=(-y)/(-12-0)=1/(-2+3)`

`⇒ x/(45)= (-y)/-12=1/1`

`⇒ x/45=y/12=1`

`⇒ x = 45, y=12`

Hence, the present age of father is 45 years and the present age of son is 12 years.