### Three vessels whose capacities are in the ratio of 3 : 2 : 1 are completely filled with milk mixed with water. The ratio of milk and water in the mixture of vessels are 5 : 2, 4 : 1 and 4 : 1 respectively. Taking $\large\frac{1}{3}$ of first, $\large\frac{1}{2}$ of second and $\large\frac{1}{7}$ of third mixture, a new mixture kept in a new vessel is prepared. The percentage of water in the new mixture is.

A. 32% B. 28% C. 30% D. 24% Answer: Option D

### Solution(By Apex Team)

$\begin{array}{l}3:2:1\\ \text{ M:W }\quad\text{ T Mixture }\\ \mathrm{V}-1\rightarrow(5:2=7)_{\times5}\\ \mathrm{V}-2\rightarrow(4:1=5)_{\times7}\\ \mathrm{V}-3\rightarrow(4:1=5)_{\times7}\\ \text{Equate the mixture}\\ \text{ M:W T Mixture }\\ (\mathrm{V}-1)\rightarrow25:10\quad=35\\ (\mathrm{V}-2)\rightarrow28:7=35\\ (\mathrm{V}-3)\rightarrow28:7=35\\ \text{ Capacities }\quad\mathrm{M}:\mathrm{W}=\text{ Total Mix. }\\ (\mathrm{V}-1)\times3\rightarrow75:30=105\\ (\mathrm{V}-2)\times2\rightarrow56:14=70\\ (\mathrm{V}-1)\times1\rightarrow28:7=35\\ \end{array}$ \begin{aligned}&\text{Water taken out}\\ &\Rightarrow\frac{1}{3}\text{ of water in }(\mathrm{V}-1)+\frac{1}{2}\text{ of water in }(\mathrm{V}-2)+\frac{1}{7}\text{ of water in }(\mathrm{V}-3)\\ &\Rightarrow\frac{1}{3}\times30+\frac{1}{2}\times14+\frac{1}{7}\times7\\ &\Rightarrow10+7+1\\ &\Rightarrow18\\ &\text{Similarly mixture will be}\\ &\Rightarrow\frac{1}{3}\times105+\frac{1}{2}\times70+\frac{1}{7}\times35\\ &\Rightarrow75\\ &\therefore\%\text{ of water }=\frac{18}{75}\times100\\ &=24\%\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

A. 1 : 2
B. 1 : 3
C. 2 : 1
D. 3 : 1