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      Question

      A tank has two inlet pipes P and Q. Pipe P can fill 12

      liters in 4 hours and pipe Q can fill 30 liters in 5 hours. If P is opened for 2 hours and then closed, after which Q is opened for the next 1 hour and this 3-hour pattern is repeated, then in how much time will the tank of capacity 96 liters be completely filled?
      A 24 hrs Correct Answer Incorrect Answer
      B 30 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 12 liters in 4 hours ⇒ P’s efficiency = 12/4 = 3 liters/hour Q fills 30 liters in 5 hours ⇒ Q’s efficiency = 30/5 = 6 liters/hour Working pattern: • First 2 hours: P alone → water filled = 3 × 2 = 6 liters • Next 1 hour: Q alone → water filled = 6 × 1 = 6 liters So, in 3 hours, total water filled = 6 + 6 = 12 liters Tank capacity = 96 liters Number of 3-hour cycles required = 96 ÷ 12 = 8 Total time taken = 8 × 3 = 24 hours

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