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      Question

      P and Q together can complete 75% of a work in 15 days

      while Q alone takes 40% more time than P and Q together to complete the whole work. Find the time taken by P alone to complete 90% of the work.
      A 75 days Correct Answer Incorrect Answer
      B 40 days Correct Answer Incorrect Answer
      C 90 days Correct Answer Incorrect Answer
      D 63 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Time taken by P and Q together to complete the whole work = 15/0.75 = 20 days Time taken by Q alone to complete the whole work = 1.40 × 20 = 28 days Total work = 140 units (LCM of 20 and 28) Amount of work done by P and Q together in one day = 140/20 = 7 units Amount of work done by Q alone in one day = 140/28 = 5 units Amount of work done by P alone in one day = 7 – 5 = 2 units Desired time = (0.90 × 140)/2 = 63 days

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