From a cask of milk containing 64 litres, 8 litres are drawn out and the cask is filled up with water. If the same process is repeated a second, then a third time, what will be the proportion of milk to water in the resulting mixture?

Correct option is D

Total amount = 64 litres,
8 litres are drawn out and the cask is filled up with water.
The same process is repeated a second, then a third time,
The final quantity of the original mixture = [ Initial amount( 1 - the amount taken out / Initial amount)n]
As per the formula,
The final quantity of the original milk in the mixture = [64 ( 1 - 8/64)3]
64 × 343 /512
343 / 8
The amount of water will be 64 - 343/8 = 169 / 8
The ratio will be 343 : 169