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      Question

      Two inlet pipes P and Q are used to fill a tank. Pipe P

      fills 25 liters in 5 hours and pipe Q fills 60 liters in 5 hours. Pipe P is kept open for 2 hours and then closed, and pipe Q is opened for the next 1 hour. This process is repeated. If the total capacity of the tank is 264 liters, then find the total time taken to fill the tank.
      A 24 hrs Correct Answer Incorrect Answer
      B 36 hrs Correct Answer Incorrect Answer
      C 18 hrs Correct Answer Incorrect Answer
      D 20 hrs Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, P fills 25 liters in 5 hours ⇒ P’s efficiency = 25/5 = 5 liters/hour Q fills 60 liters in 5 hours ⇒ Q’s efficiency = 60/5 = 12 liters/hour Working pattern (per 3 hours): • First 2 hours: P alone → 5 × 2 = 10 liters • Next 1 hour: Q alone → 12 × 1 = 12 liters Total filled in 3 hours = 10 + 12 = 22 liters Tank capacity = 264 liters Number of 3-hour cycles required = 264 ÷ 22 = 12 Total time taken = 12 × 3 = 36 hours

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