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

Question

The ratio of Milk to Water in Solution 1 is 4:1 and ratio of Milk to Water in Solution 2 is 3:1. Both solution 1 and 2 were mixed such that ratio of Milk to Water is 77:23. Find the ratio in which two solutions were mixed?

A) 2:3
B) 6:2
C) 3:4
D) 1:1
E) 4:5

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Official Answer

A

A) 2:3
B) 6:2
C) 3:4
D) 1:1
E) 4:5

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CrackverbalGMAT · Answer

The ratio of Milk to Water in Solution 1 is 4:1 and ratio of Milk to Water in Solution 2 is 3:1. Both solution 1 and 2 were mixed such that ratio of Milk to Water is 77:23. Find the ratio in which two solutions were mixed?

A) 2:3
B) 6:2
C) 3:4
D) 1:1
E) 4:5

Are You Up For the Challenge: 700 Level Questions

Show Answer

Official Answer

A

Let the solution 1 be X and solution 2 be Y.

Milk in Solution 1 + Milk in Solution 2 = Milk in Solution( 1+ 2)

\frac{4}{5} x + \frac{3}{4 }y = \frac{77}{100} (x + y )

80x + 75 y = 77(x + y )

3x = 2y

x/y = x : y = 2:3

Option A is the answer.

#Approach 2 Since this is an application of weighted average, we can also use allegation method to solve this question.

Thanks,
Clifin

ellewoods13 · Answer

The ratio of Milk to Water in Solution 1 is 4:1 and ratio of Milk to Water in Solution 2 is 3:1. Both solution 1 and 2 were mixed such that ratio of Milk to Water is 77:23. Find the ratio in which two solutions were mixed?

A) 2:3
B) 6:2
C) 3:4
D) 1:1
E) 4:5

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Show Answer

Official Answer

A

4x+3y/x+y=77:23
x:y=8:15

Not able to understand the flaw in this reasoning. can someone help?!

IanStewart · Answer

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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