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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 $69 \large\frac{3}{13} \%$ milk, is.

A. 2 : 7 B. 3 : 5 C. 5 : 2 D. 5 : 7 Answer: Option A
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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: $\begin{aligned}&\text{∴ Required ratio}\\ &=\frac{2}{91}\ :\ \frac{1}{13}\\ &=2\ :\ 7\end{aligned}$

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