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      Question

      A, B, and C together can do a work alone in 13 days, 52

      days, and 91 days respectively. A alone starts the work and work for 3 days and leaves the work, then B alone does the work for 8 days and leaves the work. If remaining work is done by C alone then for how many days has C worked?
      A 29 days Correct Answer Incorrect Answer
      B 17.5 days Correct Answer Incorrect Answer
      C 39 days Correct Answer Incorrect Answer
      D 47 days Correct Answer Incorrect Answer
      E 56 days Correct Answer Incorrect Answer

      Solution

      Total work = LCM of 13, 52 and 91 = 364 units Unit per day of A = 364/13 = 28 Unit per day of B = 364/52 = 7 Unit per day of C = 364/91 = 4 Units of work done by A in 3 days = 28 × 3 = 84 units Units of work done by B in 8 days = 7 × 8 = 56 units Remaining work = 364 – (84 + 56) = 224 units So, C has worked for 224/4 = 56 days

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