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?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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