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      Question

      ‘P’ and ‘Q’ can complete a task in 72 days,

      while ‘Q’ and ‘R’ can finish 60% of the same task in 27 days. If ‘R’ is twice as efficient as ‘P’, how many days will ‘R’ alone take to complete the entire task?
      A 60 days Correct Answer Incorrect Answer
      B 45 days Correct Answer Incorrect Answer
      C 25 days Correct Answer Incorrect Answer
      D 18 days Correct Answer Incorrect Answer

      Solution

      Time taken by ‘Q’ and ‘R’ to do the whole work = (27 × 100) / 60 = 45 days Let total work = LCM of 72 and 45 = 360 units Efficiency of ‘P’ and ‘Q’ = 360 / 72 = 5 units/day Efficiency of ‘Q’ and ‘R’ = 360 / 45 = 8 units/day Let efficiency of ‘P’ = y Then efficiency of ‘R’ = 2y ATQ, (Q + R) - (P + Q) = 2y - y = y = 3 ⇒ y = 3 ⇒ R’s efficiency = 2 × 3 = 6 units/day Time taken by ‘R’ = 360 / 6 = 60 days

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