Question

The average age of a husband and a wife, who were married 4 years ago, was 25 years at the time of their marriage. The average age of the family consisting of husband, wife and a child born during that interval is 20 years today. The age of the child is

(a) 1 year

(b) 2 years

(c) 2.5 years

(d) 3 years

Answer 1

Correct option is (b) 2 years

Given that, 4yrs. back, the average age of a couple = 25yrs.

Then, the total = 25 × 2yrs. = 50yrs.

After 4yrs. the sum will increase by 4 × 2yrs. = 8yrs.

Let the child's age = xyrs.

Then the total age of the family = (50 + 8 + x)yrs = (58 + x)yrs.

Then, by the given condition,

\(\frac{58 +x}3 = 20\)

⇒ 58 + x = 60

⇒ x = 2yrs.

Answer 2

(H + W)/2 = 25  or H + W = 50

(H + 4 + W + 4 + C)/3 = 20   or H + W + 8 + C = 60

Substitute "50" for "H + W" in the second equation:  50 + 8 + C = 60

Therefore the age of the child is: (b) 2 years