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    Question

    Pipes A, B, and C can fill a tank in 10 hours, 5 hours,

    and 20 hours respectively. If the efficiencies of pipes A and B are each reduced by 50% of their original efficiency and all three pipes are opened together, find the total time taken by them to fill the tank.
    A 10 hrs Correct Answer Incorrect Answer
    B 5 hrs Correct Answer Incorrect Answer
    C 12 hrs Correct Answer Incorrect Answer
    D 18 hrs Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the capacity of the tank (LCM of 10, 5, and 20) be 20 liters. Efficiency of pipe A = 20/10 = 2 liters/hour Efficiency of pipe B = 20/5 = 4 liters/hour Efficiency of pipe C = 20/20 = 1 liter/hour New efficiency of pipe A = 2 × (50/100) = 1 liter/hour New efficiency of pipe B = 4 × (50/100) = 2 liters/hour Total efficiency = 1 + 2 + 1 = 4 liters/hour Required time = 20 / 4 = 5 hours

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