Age puzzle using present age difference: “I was your present age when you were born.” Father is 36 now—boy’s age five years ago?
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A13
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B15
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C17
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D20
Answer
Correct Answer: 13
Explanation
Introduction / Context:Classic age-word problem: a statement relates the father’s age at the son’s birth to the son’s present age. Translate into an equation using the constant age difference between parent and child.
Given Data / Assumptions:
- Father’s current age = 36.
- Let the son’s current age = s.
- Father says: “I was of your present age when you were born.”
- Find the son’s age 5 years ago = s − 5.
Concept / Approach:At the son’s birth, the father’s age equals the son’s current age s. The present age difference equals the father’s age at that time: father_now − son_now = s. Solve for s directly.
Step-by-Step Solution:
Set up equation: 36 − s = s.Solve: 36 = 2s ⇒ s = 18.Five years ago, the boy’s age = 18 − 5 = 13.Verification / Alternative check:If the son is 18 now, then 18 years ago (at son’s birth) the father was 18 (matching the son’s current age). This confirms the condition.
Why Other Options Are Wrong:
- 15, 17, 20: These correspond to current ages 20, 22, 25 respectively, which contradict the father’s statement when checked.
Common Pitfalls:Interpreting the quote as a sum rather than a difference, or forgetting that the parent-child age gap is constant.
Final Answer:13