Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
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)$\frac{1}{3}$
(b)$\frac{1}{4}$
(c)$\frac{2}{3}$
(d)$\frac{3}{4}$
Answer
Answer (as printed): A
Explanation
Let the quantity of wine and water in the original mixture be $3 x$ and $x$ litres only. Total quantity of the mixture $=(3 x+x)$ litres $=4 x$ litres. Let $y$ litres of the mixture be replaced by water. Quantity of wine in $y$ litres of mixture $=\left(\frac{3 y}{4}\right)$ litres. Quantity of water in $y$ litres of mixture $=\left(\frac{y}{4}\right)$ litres. $$\therefore \quad 3 x-\frac{3 y}{4}=x-\frac{y}{4}+y \Rightarrow 2 x=\frac{3 y}{2} \Rightarrow 4 x=3 y .$$ Required fraction $=\frac{y}{4 x}=\frac{1}{3}$.
Explanation as extracted from the printed page; notation may be imperfect.