Two vessels contain mixtures of milk and water in the ratio of 8 : 1 and 1 : 5 respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture must be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?

Let the mixture drawn from 1st vessel be $$9x$$ gallons and from 2nd vessel be $$6y$$ gallons

Now, in the third vessel (26 gallons), quantity of milk = 13 gallons and water = 13 gallons

According to ques, milk from first two vessels = $$8x+y=13$$ --------------(i)

and water = $$x+5y=13$$ -------------(ii)

Solving the two equations, we get : $$x=\frac{4}{3}$$ and $$y=\frac{7}{3}$$

$$\therefore$$ Mixture taken from second vessel = $$6\times\frac{7}{3}=14$$ gallons

=> Ans - (B)