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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 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? Correct Answer 10 hours

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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