UPSC Prelims 2004 Q96: Science & Technology – Quantitative Aptitude
Two cars X and Y start from two places A and B respectively which are 700 km apart at 9 a.m.
Both the cars run at an average speed of 60 km/hr. Car X stops at 10 a.m. and again starts at 11
a.m. while the other car Y continues to run without stopping. When do the two cars cross each
other?
- (a) 2:40 p.m.
- (b) 3:20 p.m.
- (c) 4:10 p.m.
- (d) 4:20 p.m.
Answer: (b) 3:20 p.m.
Explanation
Two cars on a 700 km route
| Time | Position |
|---|---|
| 9 to 10 a.m. | Both run 60 km; gap = 700 - 120 = 580 km |
| 10 to 11 a.m. | Only Y runs, 60 km; gap = 520 km |
| After 11 a.m. | Both run, closing at 120 km/hr: 520 / 120 = 4 h 20 min |
| Meeting time | 11:00 + 4 h 20 min = 3:20 p.m. |
Two cars X and Y start from places 700 km apart at 9 a.m. at 60 km/hr each, and car X stops for one hour; the cars meet at 3:20 p.m.
Answer: (b) 3:20 p.m.
Why each option is right or wrong
- (a) Incorrect. 2:40 p.m. ignores the one hour stop of car X.
- (b) CORRECT. They meet at 3:20 p.m.
- (c) Incorrect. 4:10 p.m. is later than the meeting time.
- (d) Incorrect. 4:20 p.m. is later than the meeting time.
Key point
Closing speed 120 km/hr; subtract the stop's effect first.
Remember
The cars cross each other at 3:20 p.m.
Common mistakes
- Forgetting that car Y keeps running during X's stop.
- Using 700/120 without adjusting for the stop.
- Counting the stop from the wrong hour.
Exam tip
Find the gap after the stop, then divide by the combined speed.
Sources
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Time and Distance)
- Arun Sharma — How to Prepare for Quantitative Aptitude for the CAT (Time, Speed and Distance)