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      Question

      Time taken by 'A', 'B' and 'C' to complete a work is 51

      days, 85 days and 102 days respectively. All of them started the work together but 'B' and 'A' left the work 19 days and 9 days respectively before the completion of work. Find the total time taken to complete the work.
      A 34 days Correct Answer Incorrect Answer
      B 26 days Correct Answer Incorrect Answer
      C 14 days Correct Answer Incorrect Answer
      D 25 days Correct Answer Incorrect Answer

      Solution

      Let the total work be 510 units (LCM of 51, 85 and 102) Efficiency of 'A' = (510/51) = 10 units/day Efficiency of 'B' = (510/85) = 6 units/day Efficiency of 'C' = (510/102) = 5 units/day Let the time taken to complete the work be 'n' days. So, (10 + 6 + 5) X (n - 19) + (10 + 5) X 10 + 5 X 9 = 510 Or, 21n - 399 + 150 + 45 = 510 Or, 21n = 714 Or, 'n' = 34

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