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    Question

    Pipes A, B, and C can fill a tank in 30 minutes, 45

    minutes, and 60 minutes respectively. All the pipes are opened together. A is closed after  n minutes, and B is closed  (2n - 2) minutes before the tank is filled. If the tank is filled in 28 minutes, find the value of  n.
    A 14 Correct Answer Incorrect Answer
    B 12 Correct Answer Incorrect Answer
    C 18 Correct Answer Incorrect Answer
    D 16 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the total capacity of tank be 180 litres (LCM of 30, 45, 60)
    Efficiency of A = 180 ÷ 30 = 6 litres/minute
    Efficiency of B = 180 ÷ 45 = 4 litres/minute
    Efficiency of C = 180 ÷ 60 = 3 litres/minute So,
    (6 + 4 + 3) × n + (4 + 3) × (28 - n - (2n - 2)) + 3 × (2n - 2) = 180
    Or, 13n + 7(30 - 3n) + 6n - 6 = 180
    Or, 13n + 210 - 21n + 6n - 6 = 180
    Or, -2n + 204 = 180
    Or, n = 12

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