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 ?
- (a) 1 only ✓ UPSC's answer
- (b) 2 only
- (c) Both 1 and 2
- (d) Neither 1 nor 2
Why the answer is (a)
• The shares of A, B and C are proportional to p, q and r, so the largest ratio gives the largest share and the smallest ratio gives the smallest share.
• If p > q + r, then p is greater than q and also greater than r, because q and r are positive parts of the ratio.
• Therefore A's share is greater than both B's and C's shares, making statement 1 correct.
• If r < p + q, r need not be less than p or less than q; for example, p = 1, q = 10, r = 5 satisfies r < p + q but C does not get the minimum share.
• Hence statement 2 is incorrect, and the official key (a) 1 only follows.
Why the other options are wrong
- (b) 2 only
- Option (b) is wrong because statement 1 is correct while statement 2 is not sufficient to make C's share minimum.
- (c) Both 1 and 2
- Option (c) is wrong because statement 2 is incorrect, so both statements are not correct.
- (d) Neither 1 nor 2
- Option (d) is wrong because statement 1 is correct, so it is not true that neither statement is correct.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.