GATE 2025 PI – Question 7
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 $a_1$ and $a_2$ (in years) denote the ages of the brothers and $a_1 < a_2$.
Which one of the following statements is correct about their age on the day when they attain the same weight?
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Correct answer: (B) $a_1 < 50 < a_2$
Explanation
On each side of 50 the function is strictly monotonic, so it takes any given value at most once on that side. Two different ages with the same weight therefore cannot both be below 50 or both be above 50. One must be below 50 (on the rising part) and the other above 50 (on the falling part). Neither can be exactly 50, because the value at 50 is the maximum and is reached only once. So $a_1 < 50 < a_2$. This is the intended interpretation with strictly increasing and decreasing portions. If “monotonically” allows plateaus, equal weights at distinct ages on the same side of 50 are possible, so strictness is an implicit source assumption.
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