Question

10 years hence, the age of father will be the twice the age of his son. If the current sum of their ages is 64 years old. Find the difference between their ages.

1. 24 years
2. 26 years
3. 28 years
4. 30 years

Answer 1

Correct Answer - Option 3 : 28 years

Given:

The sum of their ages is 64 years old

After 10 years, the age of father will be twice the age of his son

Calculations:

Let the age of father be ‘x’ years old

Let the age of son be ‘y’ years old

After 10 years,

The age of father will be (x + 10) years old

The age of son will be (y + 10) years old

According to question, we have

⇒ x + 10 = 2(y + 10)

⇒ x + 10 = 2y + 20

⇒ x – 2y = 10      ----(1)

And, x + y = 64      ----(2)

From (1) and (2), we get

⇒ y = 18 years

So, the age of son is 18 years old

Put y = 18 in equation (2), we get

⇒ x = 46 years

So, the age of father is 46 years old

Difference between their ages is

⇒ 46 – 18 = 28 years

∴ The difference between the ages of father and son is 28 years.