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    Question

    A tank is filled by 3 pipes, second pipe take 10 hours

    more than first pipe and 10 hours less than third pipe to fill the tank alone. If second and third pipe together take 2 hour more than first pipe to fill the tank then find out how much time second pipe will take to fill the tank alone?
    A 20 hours Correct Answer Incorrect Answer
    B 10 hours Correct Answer Incorrect Answer
    C 5 hours Correct Answer Incorrect Answer
    D 6 hours Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the second pipe can fill tank in x hours So, first pipe fill tank in (x-10) hours and  Third pipe fill tank in (x + 10) hours According to the question, Second pipe and third pipe together take 2 hour more time to fill the tank from first pipe. So time taken by second pipe third pipe together = (x – 10 + 2) hours = (x – 8) hours  1/x + 1/(x +10) = 1/(x -8) (x +10 + x )/(x2+ 10 x) = 1/(x - 8) (x – 8) (2x + 10) = x2+ 10x 2x2+ 10x - 16x – 80 = x2+ 10x x2 - 16x – 80 = 0 x2 - 20x + 4x – 80 = 0 x(x – 20) + 4(x – 20) = 0 (x – 20) (x + 4) = 0 x = - 4, 20 So second pipe can fill the tank in 20 hours alone.

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