UPSC Prelims 2025 CSAT, question 78

Topic: Arithmetic

Q78

The average of three numbers $p,q$ and $r$ is $k$ . $p$ is as much more than the average as $q$ is less than the average. What is the value of $r$ ?

Solution.

Answer: (a) $k$

Since the average of $p, q,$ and $r$ is $k$ , we have $p + q + r = 3k$ .
The condition that $p$ exceeds $k$ by the same amount that $q$ is less than $k$ gives $p - k = k - q \Rightarrow p + q = 2k$ .
Substituting $p + q = 2k$ into $p + q + r = 3k$ gives $r = 3k - 2k = k$ .