Question : A vessel initially contains 60 litres of milk. First, 12 litres of milk is taken out from the vessel and replaced with water. The process is repeated a second time by taking out the same amount of milk and replacing it with water. What is the final ratio of milk to water in the resultant mixture?
Option 1: 15 : 10
Option 2: 16 : 9
Option 3: 9 : 5
Option 4: 16 : 10
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Correct Answer: 16 : 9
Solution :
Given: A vessel contains 60 litres of milk.
Remaining milk = $x\left ( 1-\frac{r}{100} \right )^{n}$, Where $x$ is the total quantity, $r$ is the replacement quantity and $n$ is the number of replacements.
= $60\left ( 1-\frac{12}{60} \right )^{2}$
= $60\times \left ( \frac{4}{5} \right )^{2}$
= 38.4 litres
Water in final solution = 60 – 38.4 = 21.6 litres
Required ratio = 38.4 : 21.6 = 16 : 9
Hence, the correct answer is 16 : 9.
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