Question

The age of the father is twice the sum of the ages of his two children . After 20 years , his age will be eual to the sum of the ages of his children . Find the age of the father.

Answer 1

Let the present age of the father be x years and the sum of the present ages of his two children be y years.
Now according to the given conditions,
Case I: x = 2y
⇒ x − 2y = 0 .....(i)
Case II: After 20 years, the age of the father will be (x + 20) years and the sum of the ages of the two children will be y + 20 + 20 = (y + 40) years.
So, x + 20 = y + 40
⇒ x − y = 20 .....(ii)
Subtracting (ii) from (i), we get
− y = −20
⇒ y = 20
Putting y = 20 in (i), we get
x − 40 = 0
⇒ x = 40
Hence, the present age of the father is 40 years.