Question
A mixture contains milk and water in the ratio 7:5. If
60 liters of this mixture is replaced with 60 liters of water, the ratio of milk to water becomes 3:4. How many liters of milk are there initially in the mixture?Solution
Let the total amount of mixture be x liters. Initially, the ratio of milk to water is 7:5, so the amount of milk = (7/12) × x, and the amount of water = (5/12) × x. After 60 liters of mixture is removed, the amount of milk and water removed will be in the same ratio of 7:5. Milk removed = (7/12) × 60 = 35 liters. Water removed = (5/12) × 60 = 25 liters. Now, 60 liters of water is added, so the new amount of milk is (7/12)x - 35, and the new amount of water is (5/12)x - 25 + 60. The new ratio of milk to water is 3:4. So, (7/12)x - 35 / [(5/12)x - 25 + 60] = 3/4. Cross-multiply: 4[(7/12)x - 35] = 3[(5/12)x - 25 + 60] 4(7x - 420) = 3(5x + 420) 28x - 1680 = 15x + 1260 28x - 15x = 1680 + 1260 13x = 2940 x = 2940 / 13 liters Now, calculate the amount of milk: Milk = (7/12) × 2940/13 ≈ 132 liters Correct option: e
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