Filling a Cistern

Pipe S can fill cistern is 2 hours and pipe k can fill a cistern in 3 hours, Pipe Y can empty it in 5 hours. Supposing all the pipes are turned on when the cistern is completely empty, how long will it take to fill?

Answer: 

 1 11/19 Hours. In one hour S fills ½ K fills 1/3 and Y empties 1/5 of the cistern.

With all the pipes working (1/2 + 1/3 – 1/5)

Or 19/30 of the cistern is filled in one hour.

With all the pipes working (30 – 30)

Of the cistern is filled in (30/19) hours.