A cistern can be filled by a inlet tap in 6 hours and emptied by an outlet pipe in 8 hours. How long will it take to fill the cistern if both the tap and the pipe are opened together?

Explanation

The given details are,
Inlet tap can fill a cistern in` = 6` hours.
Inlet tap can fill a cistern in` 1` hour` = 1/6`
Outlet tap can empty the cistern in` = 8` hours.
Outlet tap can empty the cistern in` 1` hour `= 1/8`
Work done by both pipe in `1` hour` = (1/6– 1/8)`
`= (4-3)/24`
`= 1/24`
`therefore` When both tap and pipe are opened together the cistern can be filled in` = 1/(1/24) = 24` hours.