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. $$\frac{1}{4}$$
B. $$\frac{1}{3}$$
C. $$\frac{2}{3}$$
D. $$\frac{1}{2}$$
Answer: Option B
Solution(By Examveda Team)
Let the quantity of liquid drawn out = x$$\eqalign{ & \Rightarrow \frac{{3 - \frac{3}{4}x}}{{1 - \frac{1}{4}x + x}} = \frac{1}{1} \cr & \Rightarrow 12 - 3x = 4 - x + 4x \cr & \Rightarrow 8 = 6x \cr & \Rightarrow x = \frac{4}{3} \cr} $$
Hence, required part of quantity
$$\eqalign{ & {\text{ = }}\frac{{\frac{4}{3}}}{4} \cr & {\text{ = }}\frac{1}{3} \cr} $$
Related Questions on Alligation
A. $$\frac{{1}}{{2}}$$ kg
B. $$\frac{{1}}{{8}}$$ kg
C. $$\frac{{3}}{{14}}$$ kg
D. $$\frac{{7}}{{9}}$$ kg
A. 81 litres
B. 71 litres
C. 56 litres
D. 50 litres
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