Question

The son's current age is 2 years more than the one-third the age of his mother. If the average age of mother and son is 24 years, what is mother's present age?
1. 34.5 years
2. 35 years
3. 13.5 years
4. 40 years

Answer 1

Correct Answer - Option 1 : 34.5 years

Given:

The son's current age is 2 years more than the one-third the age of his mother.

The average age of the mother and son = 24 years.

Concepts used:

Average = (Sum of all observations)/(Number of observations)

Calculation:

Let the age of mother be x years and age of son be y years.

The son's current age is 2 years more than the one-third the age of his mother.

⇒ y = {(x/3) + 2}

⇒ y = (x + 6)/3

⇒ 3y = x + 6

⇒ x = 3y – 6      ----(1)

The average age of mother and son is 24 years.

Average = Sum of all observations/Number of observations

⇒ 24 = (x + y)/2

⇒ x + y = 48      ----(2)

Putting the value of x from eq (1) into eq (2),

⇒ 3y – 6 + y = 48

⇒ 4y = 48 + 6

⇒ y = 54/4 years

⇒ y = 13.5 years

Putting the value of y in eq (1),

⇒ x = 3y – 6

⇒ x = 3 × 13.5 - 6 years

⇒ y = 34.5 years

∴ The current age of mother is 34.5 years.