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      Question

      X and Y together can complete 30% of a work in 12 days

      while Y alone takes 100% more time than X and Y together to finish the whole work. Find the time taken by X alone to complete 50% of the whole work.
      A 75 days Correct Answer Incorrect Answer
      B 40 days Correct Answer Incorrect Answer
      C 90 days Correct Answer Incorrect Answer
      D 85 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Time taken by X and Y together to complete the whole work = 12/0.30 = 40 days Time taken by Y alone to complete the whole work = 2.00 × 40 = 80 days Total work = 240 units (LCM of 40 and 80) Amount of work done by X and Y together in one day = 240/40 = 6 units Amount of work done by Y alone in one day = 240/80 = 3 units Amount of work done by X alone in one day = 6 – 3 = 3 units Desired time = (0.50 × 240)/3 = 40 days

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