The milk and water in two vessels are in the ratio of 3: 1 and 7: 11 respectively. In what ratio should the liquid in both the vessels be mixed to obtain a new mixture containing half milk and half water?

Milk in 1 litre mixture of vessel 1 = $$\frac{3}{4}$$

Milk in 1 litre mixture of vessel 2 = $$\frac{7}{18}$$

Milk in 1 litre of the new mixture = $$\frac{1}{2}$$

Let ratio of liquid from both vessels be $$x:y$$

=> $$(\frac{3}{4}x)+(\frac{7}{18}y)=\frac{1}{2}(x+y)$$

Multiply both sides by L.C.M. (4,18,2) = 36

=> $$27x+14y=18x+18y$$

=> $$27x-18x=18y-14y$$

=> $$9x=4y$$

=> $$\frac{x}{y}=\frac{4}{9}=$$

$$\therefore$$ Liquid of both the vessels should be mixed in the ratio 4 : 9 such that a new mixture containing half milk and half water is obtained.

=> Ans - (B)