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

Explanation

Let the present age of father be x years.
Also, let the sum of present ages of two children be y years.
The age of father is equal to twice the sum of the ages of two children
implies x = 2 `xx` y implies x = 2y
implies x - 2y = 0 …(1)
Age of father 20 years later = (x + 20) years
Increase in age of first children in 20 years = 20 years
Increase in age of second children in 20 years = 20 years
`therefore` Increase in the age of both children in 20 years = 20 + 20 = 40 years
`therefore` Sum of ages of both children 20 years later = y + 40
Now, according to the question, we have
Father's age will be equal to sum of ages of two children (given)
implies x + 20 = y + 40
implies x - y = 20 ...(2)
implies 2y - y = 20 [( `because` x = 2y) from (1)]
implies y = 20 years
Now, x = 2y [From (1)]
implies x = 2 `xx` 20
implies x = 40
`therefore` Age of father is 40 years.