Relative Growth — “Adam is 20 and is 4 times as old as Mary. After how many years will Adam be twice Mary’s age, and what will Mary’s age be then?”
Verbal Reasoning
Problems on Ages
Difficulty: Easy
Choose an option
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A35 years
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B15 years
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C30 years
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D17 years
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E25 years
Answer
Correct Answer: 15 years
Explanation
Introduction / Context:We compare two future ages. Since Adam is currently 4 times Mary, we first get Mary’s present age, then find the time t when Adam becomes twice Mary’s age, and finally compute Mary’s age at that moment.
Given Data / Assumptions:
- Adam now = 20.
- Adam = 4 × Mary ⇒ Mary now = 5.
- In t years: Adam 20 + t; Mary 5 + t.
- Condition: 20 + t = 2(5 + t).
Concept / Approach:Solve the linear equation in t, then evaluate Mary’s age at that time.
Step-by-Step Solution:
20 + t = 10 + 2t ⇒ 10 = t.Mary then = 5 + t = 15.Verification / Alternative check:At t = 10: Adam 30, Mary 15 ⇒ Adam is exactly twice Mary.
Why Other Options Are Wrong:17/25/30/35 are not equal to 5 + 10 (the correct future age of Mary).
Common Pitfalls:Confusing “twice” with “two more,” or forgetting to add t to both ages.
Final Answer:15 years