Q30. 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?

Let the total work be the Least Common Multiple (LCM) of 8, 16, and 12, which is 48 units. Individual efficiencies: A's efficiency = 48 units / 8 days = 6 units/day B's efficiency = 48 units / 16 days = 3 units/day C's efficiency = 48 units / 12 days = 4 units/day The work pattern is A on Monday, B on Tuesday, C on Wednesday, then A on Thursday, and so on.

Work done in one 3-day cycle (Mon, Tue, Wed) = A + B + C = 6 + 3 + 4 = 13 units. Let's track the progress: - After 3 days (Mon-Wed): 13 units done. Remaining = 48 - 13 = 35 units. - After 6 days (Thu-Sat): 13 + 13 = 26 units done.

Remaining = 48 - 26 = 22 units. - After 9 days (Sun-Tue): 26 + 13 = 39 units done. Remaining = 48 - 39 = 9 units. Now, 9 units are remaining after 9 days (Tuesday). - Day 10 (Wednesday): C works.

C does 4 units. Remaining = 9 - 4 = 5 units. - Day 11 (Thursday): A works. A does 6 units/day. Since only 5 units are remaining, A will complete the work on Thursday. So, the work is finished on Day 11, which is a Thursday.

Statement 1: The work will be finished on Thursday. (Correct) Statement 2: The work will be finished in 10 days. (Incorrect, it takes 11 days) Therefore, only statement 1 is correct.