The milk and water in two vessels A and B are in the ratio 4 : 3 and 2 : 3 respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel C containing half milk and half water ?

Fraction of milk in vessel A = $$\frac{4}{7}$$

Fraction of milk in vessel B = $$\frac{2}{5}$$

Fraction of milk in vessel C = \frac{1}{2}$$

Using, rule of alligation, required ratio = $$x : y$$

$$ x : y $$

= $$\frac{4}{7} : \frac{2}{5}$$

Mean fraction : $$\frac{1}{2}$$

=> $$(\frac{1}{2}-\frac{2}{5}) : (\frac{4}{7}-\frac{1}{2})$$ [Using Alligations]

=> $$\frac{1}{10} : \frac{1}{14}$$

=> $$x : y$$ = $$\frac{1}{10} : \frac{1}{14} = 7 : 5$$