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      Question

      Pipe ‘X’ can fill a tank 15 minutes faster than Pipe

      ‘Y’. If both are opened together, they can fill the tank in 18 minutes. If 180 litres of water passes through Pipe ‘X’ in 6 minutes, what is the total capacity of the tank?
      A 850 Correct Answer Incorrect Answer
      B 765 Correct Answer Incorrect Answer
      C 900 Correct Answer Incorrect Answer
      D 952 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the time taken by Pipe ‘Y’ be N minutes

      Then, time taken by Pipe ‘X’ = (N − 15) minutes

      So, (1/N) + 1/(N − 15) = 1/18

      Or, 18 × (2N − 15) = N × (N − 15)

      Or, 36N − 270 = N² − 15N

      Or, N² − 51N + 270 = 0

      Or, N² − 45N − 6N + 270 = 0

      Or, N(N − 45) − 6(N − 45) = 0

      Or, (N − 6)(N − 45) = 0

      So, N = 6 or N = 45

      If N = 6 → X’s time = 6 − 15 = −9 → Not valid

      So, N = 45, then X’s time = 30 minutes

      Water through X in 6 minutes = 180 litres

      So, in 30 minutes, water = (180 / 6) × 30 = 900 litres

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