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 69 313\% milk, is-

Answer: Option A

Let cost of 1 litre milk be Rs. 1 Milk in 1 litre mixture in A = $$\frac{8}{13}$$ litre;
Cost price of 1 litre mixture in A = Rs. $$\frac{8}{13}$$
Milk in 1 litre mixture in B = $$\frac{5}{7}$$ litre;
Cost price of 1 litre mixture in B = Rs. $$\frac{5}{7}$$
Milk in 1 litre of final mixture
$$\begin{array}{rl}& =\frac{900}{13}\times \frac{1}{100}\times 1\\ & =\frac{9}{13}\text{ litre}\end{array}$$
Mean price = Rs. $$\frac{9}{13}$$
By the rule of alligation, we have:

∴ Required ratio = $$\frac{2}{91}$$ : $$\frac{1}{13}$$ = 2 : 7