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      Question

      ‘A’, ‘B’ and ‘C’ can

      complete a piece of work in 40 days, 45 days and 36 days, respectively. All of them started the work together but ‘A’ left the work 20 days before completion of the work while ‘C’ left the work 8 days after ‘A’ left the work. Find the approx. time taken to complete the whole work.
      A 30 days Correct Answer Incorrect Answer
      B 20 days Correct Answer Incorrect Answer
      C 40 days Correct Answer Incorrect Answer
      D 24 days Correct Answer Incorrect Answer
      E 35 days Correct Answer Incorrect Answer

      Solution

      Let, total amount of work = 360 units (LCM of 40, 45 and 36) Efficiency of ‘A’ = 360/40 = 9 units/day Efficiency of ‘B’ = 360/45 = 8 units/day Efficiency of ‘C’ = 360/36 = 10 units/day Let, the whole work is completed in ‘x’ days So, ‘A’ worked for ‘x – 20’ days And, ‘C’ worked for x – 20 + 8 = ‘x – 12’ days So, 9(x – 20) + 10(x – 12) + 8 × x = 360 => 27x = 660 => x = 24.44 ≈ 24 days

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