Problems on Ages — “Three years ago, a family of five had average age 17 years. A baby is born; now the average is still 17. Find the baby’s present age.”
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A6 month
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B9 month
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C1 years
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D2 years
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E3 years
Answer
Correct Answer: 2 years
Explanation
Introduction / Context:Average over time with changing group size is a classic twist. Carefully track the sum of ages across the time gap, accounting for everyone aging equally and the addition of a new member (the baby).
Given Data / Assumptions:
- 3 years ago: members = 5; average = 17 ⇒ sum then = 85.
- Now: members = 6 (baby added); average now = 17 ⇒ sum now = 102.
- All original five aged 3 years each over the period.
Concept / Approach:Compute the current combined age of the original five, then subtract from the current total to isolate the baby’s present age.
Step-by-Step Solution:
Sum of original five now = 85 + 5*3 = 100.Total sum now (six people) = 17 * 6 = 102.Baby’s present age = 102 − 100 = 2 years.Verification / Alternative check:If the baby were 1 year old, the total would be 101 (not 102). If 3 years, total 103 (too high). Thus 2 years is consistent.
Why Other Options Are Wrong:6 or 9 months, 1 year, or 3 years do not reconcile with both the earlier 85 and the present 102 sums.
Common Pitfalls:Forgetting to age the original members; or mistakenly averaging with 5 rather than 6 at present.
Final Answer:2 years