Question
Vessel A contains a mixture of Apple and Orange juice in
the ratio of 7:5, while Vessel B contains a mixture of Orange and Grapes juice in the ratio of 4:5. The amount of Apple juice in Vessel A is 30% less than the amount of Grapes juice in Vessel B. The overall ratio of the mixtures in Vessel A to Vessel B is x: y. Additionally, Vessel C holds a mixture of milk and water in the ratio of y: x, and Vessel D has a mixture of milk and water in the ratio of 17:8. If 50 liters from Vessel C are transferred to Vessel D, the ratio of milk to water in Vessel D changes to 49:26. Determine the quantity of milk in Vessel D.Solution
Answer: A Let Total quantity of vessel A = 12a Apple juice in vessel A = 7a Orange juice in vessel A = 5a Orange juice in vessel B = 4b Grapes juice in vessel B = 5b 7a = 70/100 * 5b a/b = 1/2 b = 2a Required the ratio (x:y)= 12a:9 * 2a = 2:3 The ratio of the milk and water in vessel C = 3:2 Milk in vessel C = 3/5 * 50 = 30 liters Water in vessel C = 2/5 * 50 = 20 liters (30 + 17z/25)/(20 + 8z/25) = 49/26 (750 + 17z) * 26 = (500 + 8z) * 49 19500 + 442z = 24500 + 392z 50z = 5000 z = 100 Milk in vessel D = 17 * 100/25 = 68 liters
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