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?
Answer & explanation
Answer: (a) k
p is above the average by exactly the amount q is below it, so p and q together total 2k. Since all three total 3k, r must equal k.
- Let p = k + d. Then q is below k by the same amount: q = k − d.
- p + q = 2k, and p + q + r = 3k because the average is k.
- So r = 3k − 2k = k.
- Check: p = 7, q = 3, r = 5 has average 5 and r equals the average.
Remember · Deviations from an average always sum to zero; equal and opposite deviations leave the third number at the average.
Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·