Question
Consider only numeric value. Quantity I: A
number is increased by 25%, and then the result is decreased by 20%. The final number is 540. What was the original number? Quantity II: A car travels 100 km at a speed of 50 km/h and the next 100 km at a speed of 60 km/h. Find the average speed of the car for the entire trip. Quantity III: A mixture contains 40 liters of alcohol and 60 liters of water. 10 liters of the mixture is taken out and replaced with 10 liters of alcohol. Find the percentage of alcohol in the new mixture.Solution
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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