A train has to complete a journey of 800 km. If it meets a minor accident, its speed becomes half of the existing speed. If there…

Question

A train has to complete a journey of 800 km. If it meets a minor accident, its speed becomes half of the existing speed. If there is a mechanical defect, the speed becomes one-fourth of the existing speed. On its way, the train meets with a minor accident after 200 km; and 400 km thereafter, it develops a mechanical defect. Had the train developed the mechanical defect after 200 km and met the minor accident 400 km thereafter, it would have taken 4 more hours to reach its destination. What was the original speed of the train in km per hour?

1. A. 200 (Correct answer)
2. B. 190
3. C. 150
4. D. 100

Correct Answer

Option A — 200

Detailed Solution & Explanation

The correct answer is Option A (200 km/h).

Key Points

• Let original speed = s. Actual run: 200 at s + 400 at s/2 + 200 at s/8 (accident then defect) = (200 + 800 + 1600)/s = 2600/s.
• Hypothetical run: 200 at s + 400 at s/4 + 200 at s/8 (defect then accident) = (200 + 1600 + 1600)/s = 3400/s.
• Difference = 800/s = 4 hours ⇒ s = 200.

Additional Information

• Applying the defect (÷4) earlier costs more time on the long 400 km stretch, and that 4-hour gap fixes the speed at Option A.