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**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 $69 \frac{3}{13} \%$ 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

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