Question

Let $a, b$ and $c$ be the ages of three persons P, Q and R respectively where $a \le b \le c$ are natural numbers. If the average age of P, Q, R is 32 years and if the age of Q is exactly 6 years more than that of P, then what is the minimum possible value of $c$?

Accepted Answer

A. Average age = 32 $\Rightarrow a + b + c = 96$. Given $b = a + 6$. To minimize $c$, we maximize $b$ (and thus $a$). Since $b \le c \Rightarrow a + 6 \le c$. $a + (a + 6) + c = 96 \Rightarrow 2a + 6 + c = 96 \Rightarrow 2a + c = 90$. Since $a + 6 \le c \Rightarrow 2a + a + 6 \le 90 \Rightarrow 3a \le 84 \Rightarrow a \le 28$. Max $a = 28 \Rightarrow b = 34$. Min $c = 96 - 28 - 34 = 34$ years.

Minimum Value of Age c

Explanation

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