Several liters of acid were drawn off 54-liter vessel full of acid and an equal amount of water was added. Again, the same volume of the mixture was drawn off and replaced by water. As a result, the vessel contained 24 liters of pure acid. How much of the acid was drawn off initially?

Using the formula for replacement, the final amount of acid is Initial Amount * (1 - Replaced Volume / Total Volume)^n. We are given the initial amount as 54 liters, the final amount as 24 liters, and n = 2. Substituting the values gives 24 = 54 * (1 - x / 54)^2. Dividing both sides by 54 yields 4/9 = (1 - x / 54)^2, so taking the square root gives 2/3 = 1 - x / 54. Solving for x gives x / 54 = 1/3, meaning x = 18. The amount of acid drawn off initially was 18 liters.

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