Question : Two vessels contain milk and water in the ratios 3 : 2 and 7 : 3. Find the ratio in which the contents of the two vessels have to be mixed to get a new mixture in which the ratio of milk and water is 2 : 1.
Option 1: 2 : 1
Option 2: 1 : 2
Option 3: 4 : 1
Option 4: 1 : 4
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Correct Answer: 1 : 2
Solution :
Given:
In the first vessel, the ratio of milk to water = 3 : 2
In the second vessel, the ratio of milk to water = 7 : 3
In the mixture vessel, the ratio of milk to water = 2 : 1
Milk in the first vessel = $\frac{3}{5}$
Milk in the second vessel = $\frac{7}{10}$
Milk in the mixture vessel = $\frac{2}{3}$
Required ratio = $ (\frac{7}{10}-\frac{2}{3}) : (\frac{2}{3} - \frac{3}{5}) =\frac{1}{30}: \frac{1}{15}=15:30 =1:2$
Hence, the correct answer is 1 : 2.
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