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      Question

      A alone can complete a piece of work in 15 days, while B

      alone can complete it in 20 days. They start the work together, and after some days A leaves. B completes the remaining work in 6 more days. For how many days did A and B work together?
      A 2 days Correct Answer Incorrect Answer
      B 6 days Correct Answer Incorrect Answer
      C 10 days Correct Answer Incorrect Answer
      D 19 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let total work = LCM(15, 20) = 60 units A’s rate = 60/15 = 4 units/day B’s rate = 60/20 = 3 units/day Together = 7 units/day Let they work together for x days, then B alone for 6 days. Work by both in x days = 7x Work by B in last 6 days = 3 × 6 = 18 Total work: 7x + 18 = 60 7x = 42 ⇒ x = 6 days

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