A man riding a bicycle covers a distance of 60 km in the direction of the wind and returns back in 8 hours. If speed of the wind…

Question

A man riding a bicycle covers a distance of 60 km in the direction of the wind and returns back in 8 hours. If speed of the wind is 10 km/hour, find the speed of the bicycle.

1. A. 25 km/hour
2. B. 20.5 km/hour
3. C. 20 km/hour (Correct answer)
4. D. 30 km/hour

Correct Answer

Option C — 20 km/hour

Detailed Solution & Explanation

The correct answer is 20 km/hour.

Key Points

• Let the bicycle's own speed be b km/h. With the wind it travels at (b + 10), against it at (b - 10).
• Total time for the 60 km each way is 8 hours: 60/(b + 10) + 60/(b - 10) = 8.
• Combining: 60(b - 10) + 60(b + 10) = 8(b² - 100) → 120b = 8b² - 800.
• Dividing by 8: b² - 15b - 100 = 0 → (b - 20)(b + 5) = 0 → b = 20 km/h (the negative root is discarded).

Additional Information

• This is the standard boats-and-streams structure, with wind replacing current: downstream speed = b + w, upstream = b - w.
• Note the trap: the average of the two leg speeds is not the answer, because equal *distances* are covered in unequal *times*.