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 𝑎1 and 𝑎2 (in years) denote the ages of the brothers and 𝑎1 < 𝑎2. Which one of the following statements is correct about their age on the day when they attain the same weight?

A.

𝑎1 < 𝑎2 < 50

B.

𝑎1 < 50 < 𝑎2

C.

50 < 𝑎1 < 𝑎2

D.

Either 𝑎1 = 50 or 𝑎2 = 50

Solution:

The weight function increases until age 50 and then decreases. So, the same weight can occur at two different ages: one before 50 and one after 50.

Since the function is the same for both brothers a1<a2a_1 < a_2, the only way they can have equal weight is if:

  • One brother is younger than 50, and

  • The other is older than 50

✅ So, the correct statement is:

a1<50<a2a_1 < 50 < a_2 → Option (B).