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      Question

      A and B together can complete a piece of work in 12

      days, while B and C together can complete the same work in 15 days. A and C together can complete the work in 20 days. If all three work together, in how many days will they complete the work?
      A 10 Correct Answer Incorrect Answer
      B 8 Correct Answer Incorrect Answer
      C 12 Correct Answer Incorrect Answer
      D 9 Correct Answer Incorrect Answer

      Solution

      Let the total work be the LCM of 12, 15, and 20, which is 60 units. Work rate of A and B together = 60 / 12 = 5 units/day. Work rate of B and C together = 60 / 15 = 4 units/day. Work rate of A and C together = 60 / 20 = 3 units/day. Adding all three equations: (A + B) + (B + C) + (A + C) = 5 + 4 + 3 = 12 units/day. Twice the combined work rate of all three (A + B + C) = 12. Work rate of A + B + C = 12 / 2 = 6 units/day. Time taken to complete the work = Total work / Combined rate = 60 / 6 = 10 days. Correct answer: a) 10

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