Problem Solving

Two vessels contain milk solutions , with milk and water in the ratio 2:11 in first vessel and in the ratio of 5:9 in the second. In what ratio should the contents of these two vessels be mixed such that resultant mixture has milk and water in the ratio 3:8 ?
a) 169/238 b) 238/169 c)138/269 d)269/138

sukhman wrote:Two vessels contain milk solutions , with milk and water in the ratio 2:11 in first vessel and in the ratio of 5:9 in the second. In what ratio should the contents of these two vessels be mixed such that resultant mixture has milk and water in the ratio 3:8 ?
a) 169/238 b) 238/169 c)138/269 d)269/138

vessel A: milk and water in the ratio 2:11
vessel B: milk and water in the ratio 5:9

Amount taken from A = x
Amount taken from B = y

(2/13)x + (5/14)y = (3/11)(x+y)

(2/13)x - (3/11)x = (3/11)y - (5/14)y

(22x - 39x)/143 = (42y - 55y)/154

17x/143 = 13y/154

x/y = 169/238

Therefore we take 169 from A and 238 from B to make the resulting solution

Ans = A