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A vessel has 500 litres of milk. 50 litres of the contents are taken out and replaced with 50 litres of…

Milk is 72.9% at the end. Each operation removes one-tenth of the mixture, so the milk left is multiplied by \(\frac{9}{10}\) each time. After three operations, milk = 500 ×…

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A vessel has 500 litres of milk. 50 litres of the contents are taken out and replaced with 50 litres of water. If this operation is repeated 2 more times, what is the percentage of milk in the vessel at the end?

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Milk is 72.9% at the end. Each operation removes one-tenth of the mixture, so the milk left is multiplied by 910\frac{9}{10} each time. After three operations, milk = 500 × (0.9)3(0.9)^{3} = 500 × 0.729 = 364.5 litres, which is 72.9% of 500 litres. 81% is the figure after only two operations, and 70% wrongly subtracts 10% three times.

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