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A and B together can complete a work in 12 days, B and C together can complete the same work in 8 days and A and C together can complete it in 16 days. In total, how many days do A, B and C together take to complete the same work?Options3 5/123 9/137 5/127 5/13

Question

A and B together can complete a work in 12 days, B and C together can complete the same work in 8 days and A and C together can complete it in 16 days. In total, how many days do A, B and C together take to complete the same work?Options3 5/123 9/137 5/127 5/13

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Solution

To solve this problem, we need to find the rates at which A, B, and C work.

Step 1: Find the rates of (A+B), (B+C), and (A+C)

  • A and B together can complete the work in 12 days, so their combined rate is 1/12 work/day.
  • B and C together can complete the work in 8 days, so their combined rate is 1/8 work/day.
  • A and C together can complete the work in 16 days, so their combined rate is 1/16 work/day.

Step 2: Add the rates of (A+B), (B+C), and (A+C)

  • (A+B) + (B+C) + (A+C) = (1/12) + (1/8) + (1/16) = 1/4 work/day.

Step 3: Notice that when we add the rates, we're counting the rates of A, B, and C twice. So, the rate of (A+B+C) is half of the total rate we calculated.

  • (A+B+C) = (1/4) / 2 = 1/8 work/day.

Step 4: To find out how many days A, B, and C together take to complete the work, we take the reciprocal of their combined rate.

  • 1 / (1/8) = 8 days.

So, A, B, and C together take 8 days to complete the work.

This problem has been solved

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