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      Question

      A tank is filled by 3 pipes, second pipe take 5 hours

      more than first pipe and 5 hours less than third pipe to fill the tank alone. If second and third pipe together take 1 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 10 hrs Correct Answer Incorrect Answer
      B 8 hrs Correct Answer Incorrect Answer
      C 12 hrs Correct Answer Incorrect Answer
      D 15 hrs 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 - 5) hours and Third pipe fill tank in (x + 5) hours According to the question, Second pipe and third pipe together take 1 hour more time to fill the tank from first pipe. So time taken by second pipe third pipe together = (x – 5 + 1) hours = (x – 4) hours 1/x + 1/(x+5) = 1/(x-4) (x +5+x )/(x2+ 5x) = 1/(x-4) (x – 4) (2x + 5) = x2+ 5x 2x2+ 5x - 8x – 20 = x2+ 5x x2- 8x – 20 = 0 x2 - 10x + 2x – 20 = 0 x (x – 10) + 2 (x – 10) = 0 (x – 10) (x + 2) = 0 x = - 2, 10 So second pipe can fill the tank in 10 hours alone.

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