The ratio of Milk to Water in Solution 1 is 4:1 and ratio of Milk to

What you've done is correct, but you'd need to do another step to answer the question. If you say that the first solution has 4x liters of milk and x liters of water, then the first solution is 5x liters in total. If the second solution has 3y liters of milk and y liters of water, the second solution is 4y liters in total. We want to find the ratio of the quantities of the two solutions, so you want to find 5x/4y, and not just x/y. You found that x/y = 8/15, and if you now multiply both sides by 5/4, you'll get 5x/4y = 40/60 = 2/3, which is the right answer.

I'd use alligation (not "allegation" in an earlier post -- that means something completely different ) here; if we make each ratio out of 100, so we learn the percent milk in each solution, the first is 80% milk, the second is 75% milk, and the mixture is 77% milk. Now we just need to find the distances to the middle average on this number line:

----75---77--------80----

which is 2 to 3, and by alligation principles, that will be the ratio of our two components.

edit: I made a comment about the wording of the question, but I'd forgotten which solution was which, so I had things backwards. The question should specify what ratio it's looking for, though (ratio of first solution to second or the reverse), and the ratio in answer B is mysteriously not reduced, which you'd never see on the GMAT.

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