Question

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?

Answer 1

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.