Q: If A and B can complete a piece of work in 18 days, B and C can complete the same work in 24 days, and A and C can complete it in 36 days, how long will it take for A, B, and C to finish the work together?

A 34
B 24
C 16
D 28
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Answer: C

The work can be completed by A and B in 18 days, so the amount of work they complete in 1 day is (1/18) of the total work.

The work can be completed by B and C in 24 days, so the amount of work they complete in 1 day is (1/24) of the total work.

The work can be completed by A and C in 36 days, so the amount of work they complete in 1 day is (1/36) of the total work.

The amount of work A, B, and C complete in 1 day is the sum of the work completed by each pair in 1 day. This is (1/18) + (1/24) + (1/36) = 9/72 = 1/8 of the total work.

Since A, B, and C complete (1/16) of the total work in 1 day, it will take them 16 days to complete the entire work.

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