###
**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**

## Show Answer

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

### The ratio, in which tea costing Rs. 192 per kg is to be mixed with tea costing Rs. 150 per kg so that the mixed tea when sold for Rs. 194.40 per kg, gives a profit of 20%.

A. 2 : 5B. 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. $\large\frac{7}{9} \mathrm{~kg}$

### In a 729 liter mixture of milk and water, the ratio of milk to water is 7 : 2. to get a new mixture containing milk and water in the ratio 7 : 3, the amount of water to be added is:

A. 81 litersB. 71 liters

C. 56 liters

D. 50 liters

### In what ratio must a mixture of 30% alcohol strength be mixed with that of 50% alcohol strength so as to get a mixture of 45% alcohol strength?

A. 1 : 2B. 1 : 3

C. 2 : 1

D. 3 : 1