A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?a.24 daysb.20 daysc.18 daysd.30 days

To solve this problem, we need to find the rates at which A, B, and C work, and then use that information to find how long it will take C to complete the work alone.

Step 1: Find the combined rates of A and B, B and C, and C and A.

A and B can complete the work in 3 days, so their combined rate is 1/3 of the work per day. B and C can complete the work in 4 days, so their combined rate is 1/4 of the work per day. C and A can complete the work in 6 days, so their combined rate is 1/6 of the work per day.

Step 2: Add the three rates together.

(1/3) + (1/4) + (1/6) = 4/12 + 3/12 + 2/12 = 9/12 = 3/4

This is the rate at which A, B, and C can complete the work together, but since each pair was counted twice, we need to divide by 2 to get the rate at which A, B, and C can complete the work together.

(3/4) / 2 = 3/8

So, A, B, and C can complete 3/8 of the work per day together.

Step 3: Subtract the rates of A and B, and B and C from the combined rate of A, B, and C to find the rate at which C works.

The rate at which C works is (3/8) - (1/3) - (1/4) = 3/8 - 4/12 - 3/12 = 9/24 - 7/24 = 2/24 = 1/12

So, C can complete 1/12 of the work per day.

Step 4: Find how long it will take C to complete the work alone.

If C can complete 1/12 of the work per day, then it will take him 12 days to complete the work alone.

So, the answer is not in the options. There might be a mistake in the problem or the options.