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      Question

      'X', 'Y', and 'Z' can complete a job individually in 20

      days, 30 days, and 24 days respectively. 'Y' and 'Z' begin the task together. After 6 days, 'Z' leaves and 'X' joins 'Y' to finish the job. Determine the total number of days required to complete the task.
      A 27.2 Correct Answer Incorrect Answer
      B 12.6 Correct Answer Incorrect Answer
      C 33.5 Correct Answer Incorrect Answer
      D 10.5 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the total work be 120 units (LCM of 20, 30, and 24)

      Efficiency of 'X' = 120 ÷ 20 = 6 units/day

      Efficiency of 'Y' = 120 ÷ 30 = 4 units/day

      Efficiency of 'Z' = 120 ÷ 24 = 5 units/day

      Let the total time taken be T days.

      So, (4 + 5) × 6 + (6 + 4) × (T − 6) = 120

      ⇒ 54 + 10(T − 6) = 120

      ⇒ 54 + 10T − 60 = 120

      ⇒ 10T = 126

      ⇒ T = 12.6 days

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