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
- B.2 only
- C.Both 1 and 2
- D.Neither 1 nor 2
▶ Answer & Explanation
Correct answer: A. 1 only
In a cycle of 3 days (Monday to Wednesday), A, B, and C complete 1/8, 1/16, and 1/12 of the work respectively. Their combined work in 3 days is (1/8 + 1/16 + 1/12) = (6+3+4)/48 = 13/48 of the work. To complete the entire work (48/48), it takes approximately (48/13) * 3 days, which is about 11.08 days. On the 9th day (3 cycles), 39/48 of the work is done. The remaining work is 9/48. On the 10th day (Thursday of the 4th week), A starts working, completing 1/8 of the work. Since 1/8 = 6/48, A alone can complete the remaining 9/48 of the work in less than a full day. Thus, the work finishes on the 10th day, which is a Thursday.
Source: UPSC csat 2023