A) \[\frac{1}{4}\]
B) \[\frac{1}{3}\]
C) \[\frac{3}{4}\]
D) \[\frac{2}{3}\]
Correct Answer: B
Solution :
Let the barrel contain 4 L of mixture. \[\therefore \] Wine \[=3\text{ }L\] Water \[=1\text{ }L\] Let x L mixture is taken out. \[\therefore \] Wine in \[(4-x)L\] mixture \[=\frac{3}{4}(4-x)\] On 'adding x L water, water in mixture \[=(4-x)\times \frac{1}{4}+x=1-\frac{x}{4}+x\] \[=\frac{4-x+4x}{4}=\frac{4+3x}{4}\] \[\therefore \] \[\frac{3}{4}(4-x)=\frac{4+3x}{4}\] \[\Rightarrow \] \[3-\frac{3x}{4}=1+\frac{3x}{4}\] \[\Rightarrow \] \[2=\frac{6x}{4}\] \[\Rightarrow \] \[x=\frac{2\times 4}{6}=\frac{4}{3}\] \[\therefore \] Required answer \[=\frac{\frac{4}{3}}{4}=\frac{1}{3}\]
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