UPSC Prelims 2003 Q132: Science & Technology – Quantitative Aptitude
Total time taken by a person in going to a place by walking and returning on cycle is 5
hours 45 minutes. He would have gained 2 hours by cycling both ways. The time taken by him to
walk both ways is
- (a) 6 hours 45 minutes
- (b) 7 hours 45 minutes
- (c) 8 hours 15 minutes
- (d) 8 hours 30 minutes
Answer: (b) 7 hours 45 minutes
Explanation
Walking and cycling times for a journey
| Step | Time |
|---|---|
| Walk one way + cycle back | 5 h 45 min |
| Cycle both ways | 5 h 45 min - 2 h = 3 h 45 min, so one way 1 h 52.5 min |
| Walk one way | 5 h 45 min - 1 h 52.5 min = 3 h 52.5 min |
| Walk both ways | 2 x 3 h 52.5 min = 7 h 45 min |
The time taken to walk both ways is 7 hours 45 minutes.
Answer: (b) 7 hours 45 minutes.
Why each option is right or wrong
- (a) Incorrect. 6 h 45 min would give a shorter walking time.
- (b) CORRECT. 2 x 3 h 52.5 min = 7 h 45 min.
- (c) Incorrect. 8 h 15 min is more than needed.
- (d) Incorrect. 8 h 30 min is more than needed.
Key point
Walk both ways = 2 x (walk + cycle) - cycle both ways = 11 h 30 min - 3 h 45 min.
Remember
Walking both ways takes 7 hours 45 minutes.
Common mistakes
- Forgetting that the gain is on both ways.
- Halving the 5 h 45 min figure wrongly.
- Taking the gain of 2 hours as the cycling time.
Exam tip
Walk both ways = 2 x total - cycle both ways.
Sources
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Time and Distance)
- NCERT Class VIII Mathematics — Linear Equations in One Variable