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      Question

      Pipe A and pipe B can fill the empty tank in 20 hours

      and 24 hours, respectively whereas pipe C can empty the full tank ‘x’ hours. Find the value of ‘x’ if pipes A, B and C together can fill the empty tank in 15 hours.
      A 11 Correct Answer Incorrect Answer
      B 13 Correct Answer Incorrect Answer
      C 15 Correct Answer Incorrect Answer
      D 9 Correct Answer Incorrect Answer
      E 12 Correct Answer Incorrect Answer

      Solution

      Let the two numbers be ‘13a’ and ‘13b’
      ATQ;
      13a × 13b = 5070
      So, (a × b) = 30 ……………………. (1)
      Also, 13a + 13b = 143
      So, a + b = 11
      Or, a = (11 – b) …………………... (2)
      Putting value of ‘a’ in equation (1), we have
      (11 – b) × b = 30
      Or, 11b – b 2 = 30
      Or, b 2 – 11b + 30 = 0
      Or, b 2 – 6b – 5b + 30 = 0
      Or, b(b – 6) – 5(b – 6) = 0
      Or, (b – 6)(b – 5) = 0
      So, b = 6 or b = 5
      So, the two numbers are = 13 × 5 = 65 and 13 × 6 = 78
      Required difference = 78 – 65 = 13

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