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Quantity I: Let the original number be x. After increasing by 25%, the number becomes x × 1.25. After decreasing by 20%, the number becomes x × 1.25 × 0.80 = 540. Solving for x: x × 1.00 = 540, x = 540. Quantity II: Let the time taken for the first part of the journey be t1 = 100 / 50 = 2 hours. Let the time taken for the second part of the journey be t2 = 100 / 60 = 5/3 hours. Total time = 2 + 5/3 = 11/3 hours. Total distance = 100 + 100 = 200 km. Average speed = Total distance / Total time = 200 / (11/3) = 200 × 3/11 = 54.5 km/h. Quantity III: The initial mixture has 40 liters of alcohol and 60 liters of water, so the alcohol percentage is 40/100 = 40%. When 10 liters of the mixture is removed, 4 liters of alcohol and 6 liters of water are removed. Now, the mixture has 36 liters of alcohol and 54 liters of water. After adding 10 liters of alcohol, the new quantity of alcohol is 36 + 10 = 46 liters. The new total mixture is 100 liters. The new alcohol percentage = 46/100 = 46%. Comparing the quantities: Quantity I = 540, Quantity II ≈ 54.5 km/h, Quantity III = 46%. Answer: (D) Quantity I > Quantity II > Quantity III
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