Question
A vessel contains a mixture of milk and water in the
ratio 3: 2. If 10 liters of the mixture are taken out and replaced with 10 liters of water, the ratio of milk to water becomes 2: 3. What is the total volume of the mixture in the vessel?Solution
Let the total volume of the mixture be 5x liters (since the ratio is 3: 2). Initially, quantity of milk = 3x liters, and water = 2x liters. After removing 10 liters of the mixture and adding 10 liters of water: Milk left = 3x - 6 liters. Water left = 2x + 6 liters. New ratio = (3x – 6): (2x + 6) = 2: 3. Cross-multiplying and solving: 9x - 18 = 4x + 12 5x = 30 x = 6 Total volume of the mixture = 5x = 30 liters.
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