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A cistern can be filled by a tap in 4 hours and emptied by an outlet pipe in 6 hours. How long will it take to fill the cistern if both the tap and the pipe are opened together?

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Inlet tap can fill a cistern in = 4 hours 

Outlet tap can emptied it in = 6 hours

 ∵ Work done by inlet tap in 1 hour \(=\frac{1}{4}\)

∵ Work done by outlet pipe in 1 hour \(=\frac{1}{6}\)

∴ Work done by both pipe in 1 hour \(=[{\frac{1}{4}-\frac{1}{6}}]=\frac{3-2}{12}=\frac{1}{12}\)

Hence, both the tap can filled it in \(\frac{1}{\frac{1}{12}}\)=12 hours

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