Two vessels contain mixtures of milk and water

Mo2men wrote:Two vessels contain mixtures of milk and water in the ratio of 4:9 in the first vessel and in the ratio of 2:7 in the second vessel. In what ratio should the contents be mixed such that the resultant mixture has milk and water in the ratio of 2:5.

A) 1:2
B) 2:1
C)18:7
D) 21:17
E) 26:9

OA: E

We can let the amount of milk and water be 4x and 9x, respectively, in the first vessel. Likewise, we can let the amount of milk and water be 2y and 7y, respectively, in the second vessel. Therefore, we have:

(4x + 2y)/(9x + 7y) = 2/5

5(4x + 2y) = 2(9x + 7y)

20x + 10y = 18x + 14y

2x = 4y

x = 2y

So the amount of mixture in the first vessel, in terms of y, is 4(2y) + 9(2y) = 26y, and the amount of mixture in the second vessel is 2y + 7y = 9y. Therefore, the ratio of the contents in the first vessel to the second vessel is 26y/(9y) = 26/9.

Answer: E