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)

• Calculate the daily work rates: A does 1/8, B does 1/16, and C does 1/12 of the work per day.

• Determine the work done in the first 3 days (Mon-Wed): 1/8 + 1/16 + 1/12 = 6/48 + 3/48 + 4/48 = 13/48.

• Calculate the work done in the next 3 days (Thu-Sat): A (1/8) + B (1/16) + C (1/12) = 13/48, bringing the total to 26/48.

• Calculate the work done in the next 3 days (Sun-Tue): A (1/8) + B (1/16) + C (1/12) = 13/48, bringing the total to 39/48.

• On the 10th day (Wednesday), C works and adds 1/12 (4/48), making the total 43/48.

• On the 11th day (Thursday), A works; since 43/48 + 1/8 (6/48) = 49/48 > 1, the work is completed on Thursday, making statement 1 correct and statement 2 incorrect.

Why the other options are wrong

(b) 2 only: The work is completed on the 11th day, not the 10th, so statement 2 is false.
(c) Both 1 and 2: Statement 2 is incorrect because the work takes 11 days, not 10.
(d) Neither 1 nor 2: Statement 1 is correct because the work is indeed finished on a Thursday.

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.