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The average age of father, mother, son and daughter is 16 years. Father is 5 times as old as the son and mother is 6 times as old as the daughter. After 3 years from now, mother will be thrice as old as the son. What is the present age of the father?

The average age of father, mother, son and daughter is 16 years. Father is 5 times as old as the son and mother is 6 times as old as the daughter. After 3 years from now, mother will be thrice as old as the son. What is the present age of the father? Correct Answer 30 years

Given:

The average age of father, mother, son and daughter is 16 years.

Father is 5 times as old as the son and the mother is 6 times as old as the daughter.

After 3 years from now, mother will be thrice as old as the son.

Concept Used:

Sum of ages = Average age × Number of members

Calculation:

Sum of the present age of father, mother, son and daughter is 16 × 4 = 64 years

Let, the age of the son is x

⇒ The age of the father is 5x

After 3 years age of the son will be (x + 3)

⇒ The age of the mother will be 3 × (x + 3) = (3x + 9)

⇒ The present age of the mother is (3x + 9) - 3 = (3x + 6) years

Accordingly, The age of the mother is 6 times age of the daughter

⇒ The age of the daughter is (3x + 6)/6 years

Accordingly,

x + 5x + (3x + 6) + (3x +6)/6 = 64

⇒ 6x + 30x + 18x + 36 + 3x + 6 = 64 × 6

⇒ 57x = 342

⇒ x = 6

Present age of the father is 5x = 5 × 6 = 30 years

∴ The present age of the father is 30 years.

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