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?

1. A. 1 Only
2. B. 2 Only
3. C. Both 1 and 2
4. D. Neither 1 nor 2

Answer: A

Explanation

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.