Numerical answer
A container holds 80 litres of pure milk. 20 litres of the mixture is withdrawn and replaced with water; this operation is repeated once more (a total of two withdraw-and-replace operations). How many litres of pure milk remain in the container after the second operation?
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Answer: 45
For repeated dilution, the milk remaining after n operations = Initial×(1 − withdrawn/total)ⁿ. Here Initial = 80 L, withdrawn each time = 20 L, total = 80 L, n = 2. Milk left = 80×(1 − 20/80)² = 80×(0.75)² = 80×0.5625 = 45 litres. This is the standard 'repeated dilution' formula — each operation multiplies the milk quantity by the same fraction (3/4 here), since the removed 20 L mixture always has the same milk concentration as the container at that moment.
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