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    Question

    Three pipes A, B, and C can fill a tank in 24 minutes,

    36 minutes, and 48 minutes respectively. All are opened together. A is closed after 'n' minutes, and B is closed (2n - 4) minutes before the tank is filled. If the tank is filled in 20 minutes, find the value of 'n'.
    A 14 Correct Answer Incorrect Answer
    B 20 Correct Answer Incorrect Answer
    C 18 Correct Answer Incorrect Answer
    D 6 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the total capacity of tank be 144 litres (LCM of 24, 36, 48)
    Efficiency of A = 144 ├╖ 24 = 6 litres/minute
    Efficiency of B = 144 ├╖ 36 = 4 litres/minute
    Efficiency of C = 144 ├╖ 48 = 3 litres/minute So,
    (6 + 4 + 3) ├Ч n + (4 + 3) ├Ч (20 - n - (2n - 4)) + 3 ├Ч (2n - 4) = 144
    Or, 13n + 7(24 - 3n) + 6n - 12 = 144
    Or, 13n + 168 - 21n + 6n - 12 = 144
    Or, -2n + 156 = 144
    Or, n = 6

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