Question

The average age of a couple is 25 years. The average age of the family just after the birth of the first child was 18 years. The average age of the family just after the second child was born was 15 years. The average age of the family after the third and the fourth children (who are twins) were born was 12 years. If the present average age of the family of six persons is 16 years, how old is the oldest child?

• A. 6 years
• B. 7 years
• C. 8 years
• D. 9 years

Hint:

Multiply average by number of members at each step and subtract backwards to find age difference at each stage.

Answer 1

The Correct Option is D

Let total ages now = \(6 \times 16 = 96\)
Couple = \(2 \times 25 = 50\)
So children’s combined age = \(96 - 50 = 46\)
Let x be age of eldest child. Through backwards average computation, we find:
- Age added by 1st child = 3×18 − 2×25 = 54 − 50 = 4 ⇒ age of first child then = 4
- Age added by 2nd child = 4×15 − 3×18 = 60 − 54 = 6 ⇒ second child was newborn
- After twins, 6×12 − 4×15 = 72 − 60 = 12 ⇒ both twins were newborn (combined age = 0)
Now, total of children’s current ages = 46
So first child = 9 (4 years old then + 5 years), and others = 8, 7, 7 (twins 7?)
Hence, oldest = {9 years}