 ### 8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?

A. 18 litres B. 24 litres C. 32 litres D. 42 litres Answer: Option B

### Solution(By Apex Team)

Let the quantity of the wine in the cask originally be x litres. Then, quantity of wine left in cask after 4 operations \begin{aligned}&=\left[x\left(1-\frac{8}{x}\right)^4\right]\text{ litres }\\ &\therefore\left(\frac{x\left(1-\left(\frac{8}{x}\right)\right)^4}{x}\right)=\frac{16}{81}\\ &\Rightarrow\left(1-\frac{8}{x}\right)^4=\left(\frac{2}{3}\right)^4\\ &\Rightarrow\frac{x-8}{x}=\frac{2}{3}\\ &\Rightarrow3x-24=2x\\ &\Rightarrow x=24\text{ litres }\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