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      Question

      A contractor assigned a job to three persons A, B and C.

      β€˜A’ which is 25% less efficient than β€˜B’ can complete 20% of a work in 8 days. β€˜C’ takes 10 days more than β€˜B’ to complete the same work. β€˜A’ and β€˜B’ started working together and after 4 days C joined them. Due to some personal emergency β€˜A’ left after 5 more days and rest of the work is completed by 'B' and 'C', together. Find the total time taken to complete the whole work.
      A 11 days Correct Answer Incorrect Answer
      B 18 days Correct Answer Incorrect Answer
      C 15 days Correct Answer Incorrect Answer
      D 10 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Time taken by β€˜A’ to complete the work alone = 8/0.2 = 40 days Time taken by β€˜B’ to complete the work alone = 0.75 Γ— 40 = 30 days Time taken by β€˜C’ to complete the work alone = 30 + 10 = 40 days Let, the total work = 120 units Efficiency of β€˜A’ = 120/40 = 3 units/day Efficiency of β€˜B’ = 120/30 = 4 units/day Efficiency of β€˜C’ = 120/40 = 3 units/day Work completed in 4 days = 4 Γ— (3 + 4) = 28 units Work completed in next 5 days = 5 Γ— (3 + 4 + 3) = 50 units Time taken by β€˜B’ and β€˜C’ to complete remaining work together = (120 – 78)/7 = 6 days Therefore, total time taken = 4 + 5 + 6 = 15 days

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