Question
Quantity 1 : A 120-liter container is filled with a
mixture of milk and water in the ratio 5:3. If 40 liters of this mixture is replaced with pure water, what is the final ratio of milk to water in the container? Quantity 2 : A 160-liter container is filled with a mixture of milk and water in the ratio 3:2. If 50 liters of this mixture is replaced with pure water, what is the final ratio of milk to water in the container?Solution
For Quantity 1 : Initial milk in the container = (5/8) × 120 = 75 liters Initial water in the container = (3/8) × 120 = 45 liters After removing 40 liters of mixture: Milk removed = (5/8) × 40 = 25 liters Water removed = (3/8) × 40 = 15 liters Remaining milk = 75 - 25 = 50 liters Remaining water = 45 - 15 = 30 liters Water added = 40 liters Final water = 30 + 40 = 70 liters Final ratio of milk to water = 50:70 = 5:7 Quantity 1 = 5:7 = 0.71 For Quantity 2 : Initial milk in the container = (3/5) × 160 = 96 liters Initial water in the container = (2/5) × 160 = 64 liters After removing 50 liters of mixture: Milk removed = (3/5) × 50 = 30 liters Water removed = (2/5) × 50 = 20 liters Remaining milk = 96 - 30 = 66 liters Remaining water = 64 - 20 = 44 liters Water added = 50 liters Final water = 44 + 50 = 94 liters Final ratio of milk to water = 66:94 = 33:47 Quantity 2 = 33:47 = 0.70 Correct option : a) Quantity 1 > Quantity 2
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