### 3 L water is taken out from vessel full of water and substituted by pure milk. This process is repeated two more times. Finally, the ratio of milk and water in the solution becomes 1728 : 27. Find the volume of the original solution.

A. 3 L B. 5 L C. 4 L D. 9 L Answer: Option C

### Solution(By Apex Team)

We use formula for it where n = number of time process of out going repeated. y = Out going milk in process. x = Volume of original solution. F = Final milk left in mixture. \begin{aligned}&F=x\left(1-\frac{y}{x}\right)^n\\ &\text{ Final quantity of water, }\\ &F=x\left(1-\frac{3}{x}\right)^3\\ &\frac{F}{x}=\left(\frac{x-3}{x}\right)^3\\ &\frac{27}{1728}=\left(\frac{x-3}{x}\right)^3\\ &\left(\frac{3}{12}\right)^3=\left(\frac{x-3}{x}\right)^3\\ &\frac{3}{12}=\frac{x-3}{x}\\ &x=4\mathrm{~L}\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