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 ages of his two children’s be y and z years.

The present age of father is three times the sum of the ages of the two children’s. Thus, we have

`x=3(y+2)`

`⇒ y+z=x/5`

After 5 years, father’s age will be (x + 5) years and the children’s age will be (y + 5) and (z + 5) years. Thus using the given information, we have

x + 5 = 2{(y + 5) + (z + 5)}

⇒ x + 5 = 2 (y + 5 + z + 5)

⇒ x = 2(y + z) + 20 - 5

⇒ x = 2 (y + z) + 15

So, we have two equations

`y+z =x/3`

x = 2(y + z) + 15

Here x, y and z are unknowns. We have to find the value of x.

Substituting the value of (y + z) from the first equation in the second equation, we have

By using cross-multiplication, we have

`x = (2x)/3+15`

`⇒ x=(2x)/3=15`

`⇒ x(1-2/3)=15`

`⇒ x/3=15`

⇒ x = 15 × 3

⇒ x = 45

Hence, the present age of father is 45 years.