Question

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

Thus, we have

x = 3(y + z)

⇒ `y + z = x/(3)`

After 5 years, the 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.