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GATE DA 2025 Q7: Brothers with the same weight function: compare ages

Question

Weight of a person can be expressed as a function of their age. The function usually varies from person to person. Suppose this function is identical for two brothers, and it monotonically increases till the age of 50 years and then it monotonically decreases. Let a1a_1 and a2a_2 (in years) denote the ages of the brothers and a1<a2a_1 < a_2.

Which one of the following statements is correct about their age on the day when they attain the same weight?

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Answer: B (official GATE 2025 final answer key)

Concept used: A function that rises then falls takes the same value at one point on each side of its peak.

First step: If both ages were on the same side of 50, the function would be strictly increasing or decreasing there, so two different ages could not give the same weight.

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Source: official GATE 2025 DA question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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