General Aptitude › Time and Work › Question #4644
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QIf 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?

ID: #4644 Time and Work 183 views
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#4644Q ID
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Time and WorkTopic
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  • A 34 ✔ ✖
  • B 24 ✔ ✖
  • C 16 ✔ ✖
  • D 28 ✔ ✖
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Explanation

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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