A cistern can be filled by a tap in 4 hours and emptied by an outlet pipe in 6hours. How long will it take to fill the cistern if both the tap and the pipe are openedtogether?
The given details are,
Inlet tap can fill a cistern in = 4 hours
Inlet tap can fill a cistern in 1 hour = 1/4
Outlet tap can empty the cistern in = 6 hours
Outlet tap can empty the cistern in 1 hour = 1/6
Work done by both pipe in 1 hour = (1/4 – 1/6)
= (3-2)/12
= 1/12
∴ When both tap and pipe are opened together the cistern can be filled in = 1/(1/12) = 12 hours.
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