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      Question

      Pipe A alone and pipe C alone can fill the empty tank in

      50% less time and 25% less time respectively than the time taken by pipe B to empty the full tank. If the time taken by pipe B alone to empty the full tank is 72 hours, then in how many hours would the tank be 84 litres filled if the pipes A, B and C are opened together?
      A 10 hours Correct Answer Incorrect Answer
      B 11 hours Correct Answer Incorrect Answer
      C 12 hours Correct Answer Incorrect Answer
      D 13 hours Correct Answer Incorrect Answer
      E 14 hours Correct Answer Incorrect Answer

      Solution

      Time taken by pipe A alone to fill the empty tank = 72 × 0.50 = 36 hours
      Time taken by pipe C alone to fill the empty tank = 72 × 0.75 = 54 hours
      Let the capacity of the tank = 216 litres (LCM of 36, 54 and 72)
      Quantity of water filled by pipe A alone in one hour = 216 / 36 = 6 litres
      Quantity of water filled by pipe C alone in one hour = 216 / 54 = 4 litres
      Quantity of water taken out by pipe B alone in one hour = 216 / 72 = 3 litres
      So the time taken to fill 84 litres of the tank = 84 / (6 + 4 – 3) = 84 / 7 = 12 hours

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