UPSC Prelims 2004 Q104: Science & Technology – Quantitative Aptitude
A and B start from the same point and in the same direction at 7 a.m. to walk around a
rectangular field 400 m × 300 m. A and B walk at the rate of 3 km/hr and 2.5 km/hr respectively.
How many times shall they cross each other if they continue to walk till 1 and 2.30 p.m.?
- (a) Not even once
- (b) Once
- (c) Twice
- (d) Thrice
Answer: (c) Twice
Explanation
> Note for students: The stem in the stored copy is garbled ('till 1 and 2.30 p.m.'), but the answer is 'twice' whether the stop time is 1:30 p.m. or 2:30 p.m., so (c) is safe.
A and B walking round a rectangular field
| Quantity | Value |
|---|---|
| Perimeter | 2 x (400 + 300) = 1,400 m = 1.4 km |
| Relative speed | 3 - 2.5 = 0.5 km/hr, same direction |
| Time between meetings | 1.4 / 0.5 = 2.8 hours |
| Meetings by 1:30 p.m. (6.5 h) or 2:30 p.m. (7.5 h) | At 2.8 h and 5.6 h: twice; the third meeting is at 8.4 h |
A gains one full round on B every 2.8 hours, so they meet at 2.8 h and 5.6 h after 7 a.m. and the third meeting would be at 8.4 hours, after the stop time, so they cross twice.
Answer: (c) Twice.
Why each option is right or wrong
- (a) Incorrect. They meet at 9:48 a.m. already.
- (b) Incorrect. A second meeting occurs at 12:36 p.m.
- (c) CORRECT. They meet at 9:48 a.m. and 12:36 p.m.
- (d) Incorrect. A third meeting would come only at 3:24 p.m.
Key point
Same direction around a track: A gains one lap on B each time they meet.
Remember
Walkers in the same direction on a loop meet when the faster gains one lap.
Common mistakes
- Using the sum of speeds for walkers in the same direction.
- Forgetting the track length is the perimeter.
- Counting the common starting point as a meeting.
Exam tip
Meeting interval = perimeter / relative 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)