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 BShow Answer
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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