A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so on. Consider the following statements : 1. The work will be finished on Thursday. 2. The work will be finished in 10 days. 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 total work is taken as the LCM of 8, 16, and 12, which is 48 units, so A completes 6 units per day, B completes 3 units per day, and C completes 4 units per day.

• The repeating cycle is A (Mon), B (Tue), C (Wed), A (Thu), B (Fri), C (Sat), A (Sun), and so on, giving 6 + 3 + 4 = 13 units of work in every 3-day cycle.

• After three full cycles (9 days, ending on Tuesday), 3 × 13 = 39 units are completed, leaving 48 − 39 = 9 units of work remaining.

• On day 10 (Wednesday), A works and completes 6 units, reducing the remaining work to 9 − 6 = 3 units.

• On day 11 (Thursday), B works and completes exactly 3 units, finishing the work; hence the work is done on Thursday, making statement 1 correct.

• Since the work is completed on the 11th day rather than the 10th, statement 2 is incorrect, and the answer is (a) 1 only.

Why the other options are wrong

(b) 2 only: Statement 2 claims the work is finished in 10 days, but after 10 days only 45 of 48 units are done; the last 3 units are completed on day 11 (Thursday) by B.
(c) Both 1 and 2: Both statements cannot be correct because the work is finished on day 11, not day 10, so statement 2 is false even though statement 1 is true.
(d) Neither 1 nor 2: Statement 1 is in fact correct: the work is completed on a Thursday (day 11), so it is wrong to say neither statement is correct.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2023, held on 28 May 2023. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.