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      Question

      ‘A’ alone can complete a piece of work in 30 days

      while ‘A’ and ‘B’ together can complete the same work in 20 days. ‘B’ started the work and after 4 days ‘A’ joined him. After 6 more days, ‘A’ left and ‘C’ joined the work and the whole work was completed in 22 days. Which one of the following statement is true?
      A If ‘A’ alone worked for 12 days and ‘B’ alone worked for 8 days then ‘C’ will complete the remaining work in 10 days. Correct Answer Incorrect Answer
      B ‘C’ can complete the whole work in 18 days if he works twice efficiently. Correct Answer Incorrect Answer
      C ‘A’ and ‘C’ together can complete 60% of the work in 8 days. Correct Answer Incorrect Answer
      D If ‘A’ alone worked for 10 days and ‘B’ alone worked for 5 days then ‘C’ will complete the remaining work in 12 days. Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Time taken by ‘A’ to complete the whole work = 30 days

      Let total amount of work = 300 units (LCM of 30 and 20)

      So, efficiency of ‘A’ = 300/30 = 10 units per day

      Efficiency of ‘A’ + ‘B’ = 300/20 = 15 units per day

      Efficiency of ‘B’ = 15 – 10 = 5 units per day

      Amount of work done by ‘B’ in 4 days = 5 × 4 = 20 units

      Amount of work done by ‘A’ and ‘B’ together in 6 days = 6 × 15 = 90 units

      Amount of work done by ‘B’ and ‘C’ together in 12 days = 300 – 20 – 90 = 190 units

      So, efficiency of ‘B’ and ‘C’ together = 190/12 ≈ 15.83 units per day

      Efficiency of ‘C’ ≈ 15.83 – 5 ≈ 10.83 units per day

      For option (a):
      Amount of work done by ‘A’ in 12 days = 12 × 10 = 120 units
      Amount of work done by ‘B’ in 8 days = 8 × 5 = 40 units
      Remaining work = 300 – 120 – 40 = 140 units
      Time taken by ‘C’ = 140/10.83 ≠ 10 days

      So, option (a) cannot be the answer.

      For option (b):
      Efficiency of ‘C’ ≈ 2 × 10.83 ≈ 21.66 units per day
      Time taken = 300/21.66 ≠ 18 days

      So, option (b) cannot be the answer.

      For option (c):
      Desired time = (0.60 × 300)/(10 + 10.83) ≠ 8 days

      So, option (c) cannot be the answer.

      Hence, option e.

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