8 litres are drawn from a container full of mango juice and is then filled with water. This operation is performed three more times. The ratio of the quantity of mango juice now left in container to that of water Is 16: 81. How much mango juice did the container hold originally?

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, \((1 - \frac{8}{x})^{4} = \frac{16}{81} \Rightarrow (1 - \frac{8}{x})^{4} = (\frac{2}{3})^{4} \Rightarrow 1 - \frac{8}{x} = \frac{2}{3} \Rightarrow \frac{8}{x} = 1 - \frac{2}{3} = \frac{1}{3} \Rightarrow x = 24\).