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    Question

    Pipes β€˜A’ and β€˜B’ can fill a tank in 6 hours and

    8 hours, respectively and pipe β€˜C’ can empty the full tank in 12 hours. All three pipes are opened together, but after 2 hours pipe β€˜B’ is closed while pipes β€˜A’ and β€˜C’ are opened until the tank is full. How many hours will the empty tank be filled this way?
    A 7 hrs Correct Answer Incorrect Answer
    B 9 hrs Correct Answer Incorrect Answer
    C 14 hrs Correct Answer Incorrect Answer
    D 12 hrs Correct Answer Incorrect Answer

    Solution

    Let the capacity of the tank be (L.C.M of 6, 8, and 12) = 24 units Efficiency of pipe β€˜A’ = 24/6 = 4 units/hour Efficiency of β€˜B’ = 24/8 = 3 units/hour Efficiency of β€˜C’ = 24/12 = 2 units/hour Effective efficiency of (A + B – C) = 4 + 3 – 2 = 5units/hour In 2 hours, part of the tank will be filled = 5 Γ— 2= 10 units Remaining part = 24 -10 = 14 units time taken to fill the remaining part of the tank by A and C = 14/2=7 Total timing =2+7 =9hours

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