Milk and Water - Mixtures

[garbage100]

Two vessels contain mixtures of milk and water in the ratio 7:4 in the first vessel and in the ratio 9:7 in the second vessel. In what ratio should these two mixtures be now mixed such that the resultant mixture has milk and water in the ratio 4:3?

Official Answer to follow soon. Please post with explanations.

[sdasar]

1st vessel has 7/11 milk and 4/11 water. If we take 'a' gallons from here, we will have 7a/11 milk and 4a/11 water.

2nd vessel has 9/16 milk and 7/16 water. If we take 'b' gallons from here, we will have 9b/16 milk and 7b/16 water.

If we mix a+b gallons, the ratio of milk to water is (7a/11 + 9b/16) / (4a/11 + 7b/16) = 4/3

112a + 99b / 64a + 77b = 4/3 ; 80a = 11b ; a/b = 11/80

[pkp]

or simply (7/11)m + (9/16)w = (4/7)(m+w) solvin got m/w = 11/80

[garbage100]

11:80 is the right answer. Thanks for the explanation guys!!