Question : The ratio of milk to water in a 100-litres mixture is 2 : 3. 10 litres of this mixture is withdrawn and replaced with milk.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%
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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