Explanation: If a container contains \(x\) litres of a pure mixture, and we take out \(y\) litres every time and replace it with water, then after \(n\) number of operations, the quantity of the original liquid left will be: \(x \times (1 - \frac{y}{x})^{n}\). Now, let the quantity of the mango juice originally be \(x\) litres. Quantity of mango juice left after 4 operations \(= x \times (1 - \frac{8}{x})^{4}\) litres. Ratio of remaining mango juice to initial quantity is: \(\frac{x \times (1 - \frac{8}{x})^{4}}{x} = (1 - \frac{8}{x})^{4}\). According to the question, this ratio equals \(\frac{16}{81}\). So, \((1 - \frac{8}{x})^{4} = \frac{16}{81} \Rightarrow (1 - \frac{8}{x})^{4} = (\frac{2}{3})^{4} \Rightarrow 1 - \frac{8}{x} = \frac{2}{3} \Rightarrow \frac{8}{x} = 1 - \frac{2}{3} = \frac{1}{3} \Rightarrow x = 24\).
