Five litres of wine is removed from a cask full of wine and is replaced with water. Five litres of this mixture is then removed and replaced with water. If the ratio of wine to water in the cask is now 16 : 9, how much wine did the cask hold?

Question: Five litres of wine is removed from a cask full of wine and is replaced with water. Five litres of this mixture is then removed and replaced with water. If the ratio of wine to water in the cask is now 16 : 9, how much wine did the cask hold?

Solution:
Let the cask holds x liters of wine.
5 liters of wine is replaced with water. This operation is done 2 times.
∴ [(x - 5)/x]² = 16/(16 + 9)
⇒ [(x - 5) / x]² = 16/25
⇒ [(x - 5)/x] = 4/5
⇒ 5x - 25 = 4x
⇒ x = 25 liters