Question : The ratio of milk to water in a 100-litres mixture is 2 : 3. 10 litres of this mixture is withdrawn and replaced with milk. This process is repeated 2 more times. What is the percentage of milk in the final mixture?
Option 1: 56.26%
Option 2: 54.27%
Option 3: 58.21%
Option 4: 51.24%
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Correct Answer: 56.26%
Solution : Proportion of water after replacement = Proportion of water before replacement × ($\frac{\text{Volume before addition}}{\text{Volume after addition}}$) (number of replacements) ⇒ Proportion of water after replacement = $\frac{3}{5} × (\frac{90}{100}$) 3 = $\frac{2187}{5000}$ So, the volume of water after replacements = $\frac{2187}{5000}$ × 100 = 43.74 litres So, the volume of milk after replacements = 100 - 43.74 = 56.26 litres Required % = $\frac{56.26}{100}\times 100$ = 56.26% Hence, the correct answer is 56.26%.
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