In a mixture, the milk and water are in the ratio 9:2. When 44 liters of the mixture is replaced with 20 liters of water, the ratio becomes 9:4. Find the initial amount of water.

ATQ, Let the initial quantities be: Milk = 9k liters Water = 2k liters Total mixture = 11k liters. Remove 44 liters of the mixture. Since the ratio is 9 : 2, the 44 liters removed has: Milk removed = 44 × (9/11) = 36 liters Water removed = 44 × (2/11) = 8 liters Remaining after removal: Milk = 9k − 36 Water = 2k − 8 Add 20 liters of water. Now: Milk = 9k − 36 Water = 2k − 8 + 20 = 2k + 12 Given final ratio milk : water = 9 : 4, (9k − 36) / (2k + 12) = 9 / 4 Cross-multiply: 4(9k − 36) = 9(2k + 12) 36k − 144 = 18k + 108 36k − 18k = 108 + 144 18k = 252 k = 14 Initial amount of water = 2k = 2 × 14 = 28 liters.