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.

#### Solution

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

⇒ `"x" - (2"x")/(3) = 15`

⇒ `"x"(1 -2/3) = 15`

⇒ `"x"/(3) = 15`

⇒ x = 15 x 3

⇒ x = 45

Hence, the present age of father is 45 years.