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 ?
- (a) k ✓ UPSC's answer
- (b) k - 1
- (c) k + 1
- (d) k/2
Why the answer is (a)
• The average of p, q, and r is k, so their sum is p + q + r = 3k.
• The condition 'p is as much more than the average as q is less than the average' means p - k = k - q.
• Rearranging this equation gives p + q = 2k.
• Substituting p + q = 2k into the sum equation yields 2k + r = 3k.
• Solving for r gives r = 3k - 2k = k.
• Therefore, the value of r is k, which corresponds to option (a).
Why the other options are wrong
- (b) k - 1
- Option (b) is incorrect because the algebraic derivation shows r equals k, not k - 1.
- (c) k + 1
- Option (c) is incorrect because the algebraic derivation shows r equals k, not k + 1.
- (d) k/2
- Option (d) is incorrect because the algebraic derivation shows r equals k, not k/2.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.