An amount of money was distributed among A, B and C in the ratio p: q: r.
Consider the following statements:
- 1.A gets the maximum share if p is greater than (q + r).
- 2.C gets the minimum share if r is less than (p + q).
Which of the above statements is/are correct?
Answer & explanation
Answer: (a) 1 only
If one part exceeds the other two combined, it certainly exceeds each of them, so A gets the most. But being less than the sum of the other two says nothing about being the smallest, as 1 : 3 : 2 shows.
- Statement 1: shares are positive, so p > q + r means p > q and p > r — A gets the maximum. Correct.
- Statement 2: take p : q : r = 1 : 3 : 2. Here r = 2 < p + q = 4, yet A, not C, gets the least. Incorrect.
- So only Statement 1 is correct.
- ✓ 1. p > q + r forces p above both q and r.
- ✗ 2. r < p + q can hold even when r is not the smallest, e.g. 1 : 3 : 2.
Remember · Test 'if … then' claims with a quick counterexample: 'greater than the sum' implies 'greatest', but 'less than the sum' does not imply 'least'.
Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·