### Two vessels A and B contain milk and water mixed in the ratio 8 : 5 and 5 : 2 respectively. The ratio in which these two mixtures be mixed to get a new mixture containing $69 \large\frac{3}{13} \%$ milk, is.

A. 2 : 7 B. 3 : 5 C. 5 : 2 D. 5 : 7 Answer: Option A

### Solution(By Apex Team)

Let cost of 1 litre milk be Rs. 1 Milk in 1 litre mixture in A = $\Large\frac{8}{13}$ litre; Cost price of 1 litre mixture in A = Rs.$\Large\frac{8}{13}$ Milk in 1 litre mixture in B = $\Large\frac{5}{7}$ litre; Cost price of 1 litre mixture in B = Rs.$\Large\frac{5}{7}$ Milk in 1 litre of final mixture \begin{aligned}&=\frac{900}{13}\times\frac{1}{100}\times1\\ &=\frac{9}{13}\text{ litre }\\ &\text{Mean price = Rs.}\frac{9}{13}\end{aligned} By the rule of alligation, we have: \begin{aligned}&\text{∴ Required ratio}\\ &=\frac{2}{91}\ :\ \frac{1}{13}\\ &=2\ :\ 7\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 liters
B. 71 liters
C. 56 liters
D. 50 liters