Two vessels A and B contain milk 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 =?

Milk in 1 litre mix. in A = $$\frac{8}{{13}}$$
Milk in 1 litre mix. in B = $$\frac{5}{{7}}$$
Milk in 1 litre of final mix. = $$\frac{{900}}{{13}} \times \frac{1}{{100}} \times 1 = \frac{9}{{13}}$$

By the rule of alligation, we have :

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