The ratio of wine and water in a drum is 3:1. | vedclass

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(B) Let the initial quantity of wine be $3x$ and water be $x$. The total volume of the mixture is $4x$.Let $y$ be the amount of mixture taken out. The

Vedclass · Accepted Answer

$\frac{1}{3}$

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(B) Let the initial quantity of wine be $3x$ and water be $x$. The total volume of the mixture is $4x$.Let $y$ be the amount of mixture taken out. The amount of wine removed is $\frac{3}{4}y$ and the amount of water removed is $\frac{1}{4}y$.After adding $y$ litres of water,the new amount of wine is $3x - \frac{3}{4}y$.The new amount of water is $x - \frac{1}{4}y + y = x + \frac{3}{4}y$.According to the problem,the new ratio is $1:1$,so:$3x - \frac{3}{4}y = x + \frac{3}{4}y$$2x = \frac{6}{4}y$$2x = \frac{3}{2}y$$y = \frac{4}{3}x$Since the total initial volume is $4x$,the fraction of the mixture replaced is $\frac{y}{4x} = \frac{4x/3}{4x} = \frac{1}{3}$.

The ratio of wine and water in a drum is $3:1$. What part of the mixture is taken out and replaced with an equal amount of water so that the ratio of wine and water in the mixture becomes $1:1$?

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