Question

The age of a father is twice that of the sum of the ages of his two sons. 20 years later, the age of the father will become the sum of the ages of his two sons. The present age of the father is 
1. 40 years
2. 60 years
3. 30 years
4. 50 years

Answer 1

Correct Answer - Option 1 : 40 years

Given:

Age of father = 2(sum of ages of his two sons)

After 20 years, Age of father = Sum of ages of his two sons

Calculation:

Let the sum of the ages of the two children and age of the father be (x + y) and F respectively.

According to question,

F = 2(x + y)      ----(i) 

After 20 years,

⇒ F + 20 = (x + 20 + y + 20) 

 ⇒ F + 20 = x + y + 40

⇒ x + y = F - 20      ----(ii)

Putting the value of (x + y) into equation (i),

F = 2(F - 20)

⇒ F = 2F - 40

⇒ F = 40

∴ The present age of father is 40 years.