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      Question

      A can complete a work in  18 days , B in  24 days ,

      and C in  36 days . A starts the work alone and works for  4 days . Then B joins him, and after  3 more days , C also joins. How many days will they take to complete the work from the beginning?
      A 10 (8/7) days Correct Answer Incorrect Answer
      B 10 (8/9) days Correct Answer Incorrect Answer
      C 11 (2/9) days Correct Answer Incorrect Answer
      D 15 (8/9) days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      A alone in 4 days = 4/18 = 2/9 A + B rate = 1/18 + 1/24 = 7/72 In next 3 days, work done = 3 × 7/72 = 21/72 Total done in 7 days = 2/9 + 21/72 = 16/72 + 21/72 = 37/72 Remaining work = 35/72 A + B + C rate = 1/18 + 1/24 + 1/36 = 4/72 + 3/72 + 2/72 = 9/72 = 1/8 Time for remaining work = (35/72) ÷ (1/8) = 35/9 days Total time = 7 + 35/9 = 98/9 = 10 (8/9) days

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