The king took a cup filled with juice and drank 1/5 of its contents. When the king looked away, the court jester refilled the cup by adding water to the remaining juice and then stirring. The king drank ¼ of this mixture. When the king looked away again, the jester refilled the cup with more water and stirred, and the king drank 1/3 of this mixture. When the king looked away a third time, the jester refilled the cup with more water. What percentage of this final mixture was water

once the king drinks 1/5 of the drink and the jester refils, the percentage of juice to water is 80% juice 20% water yes?

then 1/4 is drunk, so take 1/4 off 20% and 80% to get 15%(3/4 of 20%) and 60%(3/4 of 80%), then the jester fills the water up to 40% (as this is what is required to make up 100% of the juice).

Then 1/3 is drunk so again take this from 40% and 60% to get 26.667% water and 40% juice.

Then finally water is added to make up 100% so if the juice has depleted to 40% then the mixture is made up of 60% or 3/5 water.

hope this helps