UPSC Prelims 2007 Q147: Science & Technology – Quantitative Aptitude
- (a) 7 hours 45 minutes
- (b) 8 hours 15 minutes
- (c) 8 hours 30 minutes
- (d) 8 hours 45 minutes
Answer: (d) 8 hours 45 minutes
Explanation
Walking vs driving — time both ways
Let W = time to walk one way, C = time to drive one way.
| Situation | Equation |
|---|---|
| Walk one way + drive back = 6 h 45 min | W + C = 6 h 45 min |
| Drive both ways = 2 hours less | 2C = 4 h 45 min → C = 2 h 22.5 min |
Walk one way: W = 6 h 45 min − 2 h 22.5 min = 4 h 22.5 min.
Walk both ways: 2W = 8 h 45 min.
Shortcut: walk-both = (walk + drive) + (walk + drive) − (drive + drive) = 6:45 + 6:45 − 4:45 = 8:45.
Note: In this question bank, options (b) and (d) are both printed as "8 hours 45 minutes".
The keyed answer is (d).
Amit starts at point A, walks to point B and returns by car, taking a total of 6 hours 45 minutes; had he driven both ways, it would have taken 2 hours less. So walking both ways takes 8 hours 45 minutes.
Answer: (d) 8 hours 45 minutes.
Why each option is right or wrong
- (a) Incorrect. 7 h 45 min is an hour short of the correct 8 h 45 min.
- (b) Incorrect. 8 h 15 min is 30 minutes short of the correct 8 h 45 min.
- (c) Incorrect. 8 h 30 min is 15 minutes short of the correct 8 h 45 min.
- (d) CORRECT. Walk both ways = 2 × 6:45 − 4:45 = 8 h 45 min.
Key point
Walk both ways = 2 × (walk + drive) − (drive both ways) = 13:30 − 4:45 = 8 h 45 min.
Remember
Walking both ways takes 8 hours 45 minutes.
Common mistakes
- Answering 6:45 + 4:45 or other blind sums — set up W + C and 2C first, then solve.
- Halving the wrong total when finding the one-way driving time.
- Mixing minutes and decimal hours (2.375 h = 2 h 22.5 min).
Exam tip
Trick: (W + C) − C saved per leg. Driving both ways saves 2 hours vs (walk + drive), so walking both ways costs 2 hours more: 6:45 + 2:00 = 8:45.
Sources
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Time and Distance)
- NCERT Class VIII Mathematics — Linear Equations in One Variable