The answer to the problem is that the cask originally holds 24 liters of wine. Explanation: In the problem, we have a cask from which 8 liters of wine is drawn and this operation is performed four times in total. After these operations, the ratio of the wine left in the cask to the water is given as 16:65. This can be understood as follows: 1. Let the original quantity of wine in the cask be x liters. 2. After the first operation, the quantity of wine left in the cask is \( x - 8 \) liters. 3. The fraction of wine left after one operation is thus \( \frac{x - 8}{x} \). 4. Since the operation is performed four times, the fraction of wine left after these operations can be expressed as: \[ \left( \frac{x - 8}{x} \right)^4 = \frac{16}{81} \] (as 16 parts are wine and 65 parts are water, totaling 81 parts). 5. Setting up the equation gives: \[ \left( \frac{x - 8}{x} \right)^4 = \frac{16}{81} \] Taking the fourth root: \[ \frac{x - 8}{x} = \frac{2}{3} \] Thus, \[ 3(x - 8) = 2x \\ 3x - 24 = 2x \\ x = 24 \text{ liters} \] Hence, the initial amount of wine in the cask was indeed 24 liters【4:7†source】.