Comparative Ages — “Joan is 42, Kelvin is 26. How many years ago was Kelvin exactly half of Joan?”
Verbal Reasoning
Problems on Ages
Difficulty: Easy
Choose an option
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A6 Years
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B4 Years
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C10 Years
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D8 Years
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E12 Years
Answer
Correct Answer: 10 Years
Explanation
Introduction / Context:We look for a past time t such that Kelvin’s age then equals half of Joan’s age then. Set up a linear equation in t and solve; it is straightforward proportional reasoning with a time shift.
Given Data / Assumptions:
- Joan now = 42, Kelvin now = 26.
- t years ago: Kelvin 26 − t; Joan 42 − t.
- Target: 26 − t = (42 − t)/2.
Concept / Approach:Clear the fraction by multiplying both sides by 2, then isolate t. Ensure t is positive and realistic.
Step-by-Step Solution:
2(26 − t) = 42 − t ⇒ 52 − 2t = 42 − t ⇒ 10 = t.Verification / Alternative check:10 years ago: Kelvin 16; Joan 32; indeed 16 is half of 32.
Why Other Options Are Wrong:6/4/8/12 do not satisfy the equality when substituted for t.
Common Pitfalls:Setting 26 = 42/2 without the time shift; or subtracting t from only one person’s age.
Final Answer:10 Years