8 litres are drawn from a cask full of wine and is n filled with water. This operation is performed three more times. The ratio of quantity of wine now left in cask to that of water is 16 : 65. How much wine did cask hold originally?

Let the quantity of the wine in the cask originally be x litres.
Then, quantity of wine left in cask after 4 operations
$$\eqalign{ & = \left[ {x{{\left( {1 - \frac{8}{x}} \right)}^4}} \right]\,{\text{litres}} \cr & \therefore \left( {{{\frac{{x\left( {1 - \left( {\frac{8}{x}} \right)} \right)}}{x}}^4}} \right) = \frac{{16}}{{81}} \cr & \Rightarrow {\left( {1 - \frac{8}{x}} \right)^4} = {\left( {\frac{2}{3}} \right)^4} \cr & \Rightarrow {\frac{{x - 8}}{x}} = \frac{2}{3} \cr & \Rightarrow 3x - 24 = 2x \cr & \Rightarrow x = 24 \,\text{litres} \cr} $$