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A and B together take 6 days to complete a task. B and C together take 12 days to complete the same task. A and C together take 8 days to complete it. If A, B and C are working together, how long does it take for them to complete the task?

Correct answer: C. 5(1/3) days

  • A. 4(2/3) days
  • B. 4 days
  • C. 5(1/3) days
  • D. 1(1/3) days

Explanation

The three pair rates are 1/6, 1/12 and 1/8 work per day. Their sum is 3/8 work per day, which counts each person's rate twice, so the combined rate of A, B and C is 3/16 work per day and their time is 16/3 = 5 1/3 days. The likely trap is 4 days, caused by adding the pair rates without dividing by 2.

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About Time and Work

Problems measure work through rates, treating each person's or machine's contribution as work completed per unit time. Questions cover combined work, efficiency, wages, alternate working schedules, pipes and cisterns, and men-days relationships, with care needed to distinguish time taken by one worker from the time required when workers act together.

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