UPSC Prelims 2003 Q49: Science & Technology – Quantitative Aptitude
‘A’ walks around a circular field at the rate of one round per hour while ‘B’ runs around it at
the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m.
They shall first cross each other at
- (a) 8.30 a.m.
- (b) 8.10 a.m.
- (c) 7.48 a.m.
- (d) 7.42 a.m.
Answer: (d) 7.42 a.m.
Explanation
Two persons going round a circular field
| Quantity | Value |
|---|---|
| A's speed | 1 round per hour |
| B's speed | 6 rounds per hour |
| Relative speed (same direction) | 6 - 1 = 5 rounds per hour |
| Time to first meeting | 1/5 hour = 12 minutes, so 7:30 + 12 = 7:42 a.m. |
In the same direction B gains one round on A every 12 minutes, so they cross first at 7:42 a.m.
Answer: (d) 7.42 a.m.
Why each option is right or wrong
- (a) Incorrect. 8:30 a.m. would be after a full hour.
- (b) Incorrect. 8:10 a.m. is after 40 minutes.
- (c) Incorrect. 7:48 a.m. would be after 18 minutes.
- (d) CORRECT. 7:30 + 12 min = 7:42 a.m.
Key point
Same direction on a loop: first meeting when the faster gains one lap.
Remember
B gains a lap on A every 12 minutes, so they first cross at 7:42 a.m.
Common mistakes
- Using the sum of speeds (opposite directions).
- Dividing one hour by six rounds per hour.
- Not converting hours into minutes properly.
Exam tip
Time to first meeting = one lap divided by 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)