Question
Which of the following is the correct relation between
Quantity I and Quantity II? Quantity I: A mixture contains 40 liters of milk and 30 liters of water. 20 liters of this mixture is replaced with a mixture of milk and water in the ratio 3:2. Find the percentage of milk in the new mixture. Quantity II: A mixture contains 60 liters of milk and 40 liters of water. 30 liters of this mixture is replaced with a mixture of milk and water in the ratio 1:1. Find the percentage of milk in the new mixture.Solution
Quantity I: Initial milk = 40 liters, water = 30 liters. Amount of milk removed = (20 × 40) / 70 = 11.43 liters. Amount of water removed = (20 × 30) / 70 = 8.57 liters. New milk = 40 - 11.43 + (20 × 3) / 5 = 40 - 11.43 + 12 = 40.57 liters. New water = 30 - 8.57 + (20 × 2) / 5 = 30 - 8.57 + 8 = 29.43 liters. Total mixture = 70 liters. Percentage of milk = (40.57 / 70) × 100 = 57.96%. Quantity II: Initial milk = 60 liters, water = 40 liters. Amount of milk removed = (30 × 60) / 100 = 18 liters. Amount of water removed = (30 × 40) / 100 = 12 liters. New milk = 60 - 18 + (30 × 1) / 2 = 60 - 18 + 15 = 57 liters. New water = 40 - 12 + (30 × 1) / 2 = 40 - 12 + 15 = 43 liters. Total mixture = 100 liters. Percentage of milk = (57 / 100) × 100 = 57%. Comparing: Quantity I = 57.96% Quantity II = 57% Quantity I > Quantity II Correct option: b. Quantity I > Quantity II
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