Four years ago, the average age of a family of four persons was 18 years. During this period, a baby was born. Today if the avera…

Question

Four years ago, the average age of a family of four persons was 18 years. During this period, a baby was born. Today if the average age of the family is still 18 years, the age of the baby is

1. A. 1.2 years
2. B. 2 years (Correct answer)
3. C. 2.5 years
4. D. 3 years

Correct Answer

Option B — 2 years

Detailed Solution & Explanation

The correct answer is 2 years.

Key Points

• Four years ago the four members totalled 4 × 18 = 72 years.
• Four years later those same four have aged 4 years each, adding 16, so they now total 88 years.
• Today five people average 18, so the family totals 5 × 18 = 90 years.
• The baby's age = 90 − 88 = 2 years.

Additional Information

• The trap is forgetting that the original members have aged in the interim. Four years must be added to each of the four before the new total is compared.
• A reliable procedure for "average age changed after an addition" problems:

1. Find the old total

2. Age every original member forward by the elapsed time

3. Find the new total from the new average and new count

4. The difference is the newcomer's age

• Because the baby was born during that period, its age must be less than the four years elapsed — a quick sanity check on the answer.