GATE DA 2025 Set 1 — Question 7
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Calculus & Optimization → Analytical Aptitude → Numerical Relations & Reasoning
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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 and (in years) denote the ages of the brothers and .Which one of the following statements is correct about their age on the day when they attain the same weight?
Correct answer
(B) a₁ < 50 < a₂
Solution
Let be the weight function. It is given that is strictly increasing for and strictly decreasing for .
We are given with .
Since the function is monotonic on either side of 50, the only way for the weights to be equal at two different ages is if one age is in the increasing phase and the other is in the decreasing phase.
Therefore, must be less than 50 and must be greater than 50.
Thus, .
We are given with .
Since the function is monotonic on either side of 50, the only way for the weights to be equal at two different ages is if one age is in the increasing phase and the other is in the decreasing phase.
Therefore, must be less than 50 and must be greater than 50.
Thus, .
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