### 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

### 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}

## Related Questions On Alligation

A. 2 : 5
B. 3 : 5
C. 5 : 3
D. 5 : 2

### An alloy contains zinc, copper and tin in the ratio 2 : 3 : 1 and another contains copper, tin and lead in the ratio 5 : 4 : 3. If equal weights of both alloys are melted together to form a third alloy, then the weight of lead per kg in new alloy will be:

A. $\large\frac{1}{2} \mathrm{~kg}$
B. $\large\frac{1}{8} \mathrm{~kg}$
C. $\large\frac{3}{14} \mathrm{~kg}$
D. $\large\frac{7}{9} \mathrm{~kg}$

A. 81 litres
B. 71 litres
C. 56 litres
D. 50 litres