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      Question

      Pipe 'A' can fill a tank on its own in 14 minutes. When

      pipes 'A' and 'B' are both opened at the same time, the tank is filled in 18 minutes. Determine how long it would take for pipe 'B' alone to drain half of the tank's capacity.
      A 31.5 minutes Correct Answer Incorrect Answer
      B 25 minutes Correct Answer Incorrect Answer
      C 35 minutes Correct Answer Incorrect Answer
      D 27.5 minutes Correct Answer Incorrect Answer

      Solution

      Let the total capacity of the tank = L.C.M of 14 and 18 = 126 units So, efficiency of pipe 'A' alone = 126 ÷ 14 = 9 units/minute Combined efficiency of pipes 'A' and 'B' = 126 ÷ 18 = 7 units/minute So, efficiency of pipe 'B' alone = 7 - 9 = -2 units/minute (outlet) So, time taken by pipe 'B' alone to empty 50% of the cistern = (126 X 0.5) ÷ 2 = 31.5 minutes. Hence, option a.

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