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      Question

      'P' and 'Q' together can complete a task in 20 days. 'P'

      alone would take 12 days fewer than 'Q' to finish it. How many days would 'Q' take to do the work alone?
      A 48 days Correct Answer Incorrect Answer
      B 25 days Correct Answer Incorrect Answer
      C 32 days Correct Answer Incorrect Answer
      D 55 days Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the number of days 'Q' takes = x

      Then, time taken by 'P' = x – 12

      According to the question:

      (1/20) = (1/x) + (1/(x – 12))

      ⇒ (1/20) × x × (x – 12) = x + (x – 12)

      ⇒ x² – 12x = 20(2x – 12)

      ⇒ x² – 12x = 40x – 240

      ⇒ x² – 52x + 240 = 0

      ⇒ x² – 48x – 4x + 240 = 0

      ⇒ x(x – 48) – 4(x – 48) = 0

      ⇒ (x – 48)(x – 4) = 0

      So, x = 48 or x = 4

      Since at x = 4, P’s time becomes negative,

      x = 48

      Therefore, Q can do the work alone in 48 days.

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