A cask originally full of wine has 8 litres removed and replaced with water. This process is repeated three additional times. After these operations, the ratio of wine to water in the cask is 16:65. What was the initial volume of wine in the cask?

Explanation

Let the original volume of wine be V litres. Each time, 8 litres are removed and replaced with water, repeated 4 times in total. The ratio of wine left after these operations is given by ((V - 8)/V)^4 = 16/(16 + 65) = 16/81. Solving this equation yields V = 24 litres.