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      Question

      Worker ‘P’ can finish a task in 54 days, which is 18

      days quicker than worker ‘Q’. If they take turns daily starting with ‘P’, find the total time (in days) to complete the task.
      A 72.5 days Correct Answer Incorrect Answer
      B 44.5 days Correct Answer Incorrect Answer
      C 61.5 days Correct Answer Incorrect Answer
      D 37.5 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Time taken by 'Q' = 54 + 18 = 72 days Let total work be 216 units (LCM of 54 and 72) Efficiency of 'P' = 216 ÷ 54 = 4 units/day Efficiency of 'Q' = 216 ÷ 72 = 3 units/day Work in 2 days = 4 + 3 = 7 units Work in 60 days = 7 × 30 = 210 units Remaining work = 216 - 210 = 6 units Time by 'P' to finish remaining = 6 ÷ 4 = 1.5 days Hence, final Answer: 60 + 1.5 = 61.5 days

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