The ratio of spirit and water in the two vessels is 5 : 1 and 3 : 7 respectively. In what ratio the liquid of both the vessels should be mixed such that a new mixture containing half spirit and half water is obtained?

Spirit in 1 litre mixture of vessel 1 = $$\frac{5}{6}$$

Spirit in 1 litre mixture of vessel 2 = $$\frac{3}{10}$$

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

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

=> $$(\frac{5}{6}x)+(\frac{3}{10}y)=\frac{1}{2}(x+y)$$

Multiply both sides by L.C.M. (6,10,2) = 30

=> $$25x+9y=15x+15y$$

=> $$25x-15x=15y-9y$$

=> $$10x=6y$$

=> $$\frac{x}{y}=\frac{6}{10}=\frac{3}{5}$$

$$\therefore$$ Liquid of both the vessels should be mixed in the ratio 3 : 5 such that a new mixture containing half spirit and half water is obtained.

=> Ans - (A)