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      Question

      A alone can complete a piece of work in 12 days and B

      alone can complete the same work in 18 days.  If they work together for 4 days, then A leaves and B continues alone to finish the remaining work, in how many  total days  (from the beginning) will the work be completed?
      A 12 days Correct Answer Incorrect Answer
      B 18 days Correct Answer Incorrect Answer
      C 20 days Correct Answer Incorrect Answer
      D 24 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let total work = 1 unit. A’s rate = 1/12 work/day B’s rate = 1/18 work/day Work done together in 1 day = 1/12 + 1/18 = (3 + 2)/36 = 5/36 Work done together in 4 days = 4 × 5/36 = 20/36 = 5/9 Remaining work = 1 − 5/9 = 4/9 Now B alone does the remaining work: Time for B = (remaining work) / (B’s rate) = (4/9) ÷ (1/18) = (4/9) × 18 = 4 × 2 = 8 days Total time = 4 days (together) + 8 days (B alone) = 12 days

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