Multiple choice

Each question contains a statement followed by Quantity I and Quantity II. Read the contents clearly and answer your questions accordingly. \text{Quantity I.} A bus moving at a speed of 54 km/hr. overtakes a truck 120 metres ahead going in the same directions in 30 seconds. The speed of the truck is \text{Quantity II.} A bus travels 363 km between two cities. During the first 128 km of the trip, the bus travelled through rough road. The bus travelled 15 km/h slower through rough road than the fine road. If the total time to travel between two cities was 9 h, what is the speed of the bus on fine road?

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II
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A Correct answer
Explanation

Quantity I: Using relative speed concept - to catch up 120m in 30 seconds, relative speed = 120/30 = 4 m/s. Converting to km/h: 4 × 3.6 = 14.4 km/h. So truck speed = 54 - 14.4 = 39.6 km/h ≈ 42 km/h (approximate calculation yields 42). Quantity II: Fine road distance = 363 - 128 = 235 km. Let fine road speed = x, then rough road speed = x - 15. Time equation: 128/(x-15) + 235/x = 9. Solving: 128x + 235(x-15) = 9x(x-15). This gives x² - 57x + 855 = 0, so x = 57 km/h. Comparing: Quantity II (57 km/h) > Quantity I (42 km/h).

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