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 an.

Consider the following statements:

The work will be finished on Thursday.
The work will be finished in 10 days.

Which. of the above statements is/are correct?

EXPLANATION

Correct Option (1)

To determine the total work, the Least Common Multiple (LCM) of the individual days taken by A, B, and C is calculated. The LCM of 8, 16, and 12 is 48 units. This represents the total work.

The efficiency of each person per day is:

Work done by A = $\frac{48}{8} = 6$ units/day
Work done by B = $\frac{48}{16} = 3$ units/day
Work done by C = $\frac{48}{12} = 4$ units/day

The work pattern is A on Monday, B on Tuesday, and C on Wednesday, repeating in cycles. Therefore, in one 3-day cycle (Monday, Tuesday, Wednesday), the total work completed is:

Work in 3 days = 6 (A) + 3 (B) + 4 (C) = 13 units.

To find how many such cycles are needed for 48 units of work:

Number of full cycles = $⌊ \frac{48}{13} ⌋ = 3$ cycles.
Work completed in 3 cycles (3 x 3 = 9 days) = 3 x 13 = 39 units.
Remaining work = 48 - 39 = 9 units.

After 9 days, 39 units of work are completed. The 10th day will be a Monday (start of a new cycle), and A will work:

On Day 10 (Monday), A completes 6 units.
Work remaining = 9 - 6 = 3 units.

The 11th day will be a Tuesday, and B will work:

On Day 11 (Tuesday), B completes 3 units.
Total work completed = 39 (in 9 days) + 6 (on Day 10) + 3 (on Day 11) = 48 units.

Thus, the work is finished on the 11th day. To determine the day of the week for the 11th day, considering Day 1 is Monday:

Day 1: Monday (A)
Day 2: Tuesday (B)
Day 3: Wednesday (C)
Day 4: Thursday (A)
Day 5: Friday (B)
Day 6: Saturday (C)
Day 7: Sunday (A)
Day 8: Monday (B)
Day 9: Tuesday (C)
Day 10: Wednesday (A)
Day 11: Thursday (B)

Therefore, the work is finished on Thursday. Statement 1 is correct. The work is finished in 11 days, not 10 days, making Statement 2 incorrect.

Incorrect Options:

Options 2, 3, and 4 are incorrect because the detailed calculation demonstrates that the work is completed on the 11th day, which corresponds to a Thursday. This confirms that only statement 1 is accurate, while statement 2, asserting completion in 10 days, is false.