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A hose has three pipes. Pipe x and pipe y fill the hose and pipe z empties the hose. The pipe x can fill the tank alone in 15 hours. The pipe y can fill the same hose in 12 hours alone. The pipe z can completely empty the hose in 20 hours alone. If all the pipes are opened at the same time, how much time will it take to fill the fill the hose?

1. 10 hours
2. 12 hours
3. 8 hours
4. 6 hours

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Correct Answer - Option 1 : 10 hours


⇒ Pipe x's 1 hour's work = 1/15

⇒ Pipe y's 1 hour's work = 1/12

⇒ Pipe z's 1 hour's work = 1/20


⇒ Pipe (x + y + z)'s 1 hour's work = 1/15 + 1/12 - 1/20 = 1/10

∴ In 10 hours, hose will get completely filled if all three pipes are opened simultaneously.

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