UPSC Prelims 2006 Q95: Science & Technology – Physics
There are 8 equidistant points A, B, C, D, E, F, G and H in the clockwise direction on the
periphery of a circle. In a time - interval t, a person reaches from A to C with uniform motion while
another person reaches the point E from the point B during the same time - interval with uniform
motion. Both the persons move in the same direction along the circumference of the circle and
start at the same instant. How much time after the start will the two persons meet each other?
- (a) 4t
- (b) 7t
- (c) 9t
- (d) Never
Answer: (b) 7t
Explanation
Two persons moving round a circle
The 8 points are equidistant, so each interval between neighbouring points is one unit. Take A as position 0, B as 1, C as 2 and E as 4.
| Person | Start | Movement in time t | Speed |
|---|---|---|---|
| First (A to C) | A (position 0) | 2 units | 2 units per t |
| Second (B to E) | B (position 1) | 3 units | 3 units per t |
The second person starts 1 unit ahead and is faster by 1 unit per t. To meet again he must gain a full circle less the head start: 8 - 1 = 7 units, taking 7t.
Answer: (b) 7t.
Why each option is right or wrong
- (a) Incorrect. In 4t the faster person gains only 4 units, not the 7 needed.
- (b) CORRECT. The faster person must gain 7 units at 1 unit per t, so they meet after 7t.
- (c) Incorrect. At 9t the faster person would have gained 9 units, more than needed.
- (d) Incorrect. Their speeds differ, so they do meet.
Key point
The second person gains 1 unit per t and must cover 8 - 1 = 7 units of lead, so they meet after 7t.
Remember
Relative speed 1 unit per t; gap 7 units; they meet after 7t.
Common mistakes
- Using the full 8 units of the circle as the gap.
- Forgetting the head start of one interval.
- Assuming they never meet because they move in the same direction.
Exam tip
Same direction on a circle: time to meet = (circumference - head start) / 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)