A barrel contains a mixture of wine and water in the ratio 3 : 1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel becomes 1 : 1 ?

A. $\large\frac{1}{4}$ B. $\large\frac{1}{3}$ C. $\large\frac{2}{3}$ D. $\large\frac{1}{2}$ Answer: Option B
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Solution(By Apex Team)

Let the quantity of liquid drawn out = x $\begin{aligned}&\Rightarrow\frac{3-\frac{3}{4}x}{1-\frac{1}{4}x+x}=\frac{1}{1}\\ &\Rightarrow12-3x=4-x+4x\\ &\Rightarrow8=6x\\ &\Rightarrow x=\frac{4}{3}\end{aligned}$ Hence, required part of quantity $\begin{aligned} &=\frac{\frac{4}{3}}{4} \\ &=\frac{1}{3} \end{aligned}$

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