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-

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
$$\eqalign{ & = {\frac{{900}}{{13}} \times \frac{1}{{100}} \times 1} \cr & = \frac{9}{{13}}{\text{ litre}}{\text{}} \cr} $$
Mean price = Rs. $$\frac{9}{{13}}$$
By the rule of alligation, we have:

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