Multiple choice

Find the distance if: Quantity I: A man covers a distance in 15 hours. He covers first half at 12 km/h and second half at 15 km/h. Quantity II: Two buses moves towards each other at a speed of 30 km/h and 40 km/h respectively. When they meet it is found that faster bus covers 30 km more than slower one.

  1. Quantity II < Quantity I

  2. Quantity II > Quantity I

  3. Quantity II ≤ Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity II = Quantity I or relation cannot be established
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B Correct answer
Explanation

Quantity I: Total time = 15 hours. If distance = D, then D/2/12 + D/2/15 = 15, giving D/24 + D/30 = 15. Solving: D(1/24 + 1/30) = 15, D(9/120) = 15, D = 162 km. Quantity II: Relative speed = 70 km/h. Faster covers 30 km more, so time = 30/10 = 3 hours (since difference in speeds is 10 km/h). Total distance = 70 × 3 = 210 km. Quantity II (210) > Quantity I (162).

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