Single correct option
A and B start together from the same point on a circular track of length 1,200 m and run in the same direction at constant speeds of 8 m/s and 5 m/s respectively. If they keep running indefinitely, at how many distinct points on the track will they meet?
- A. 5
- B. 3
- C. 13
- D. 8
Show answer and solution
Answer: (B) 3
They meet whenever A has gained a whole number of laps on B. Relative speed = 8 − 5 = 3 m/s, so they meet every 1200/3 = 400 s.
In 400 s A covers 3,200 m = 2 laps + 800 m. So successive meeting points are 800 m apart along the track: 0, 800, 400 (= 1600 − 1200), then 0 again.
Hence 3 distinct meeting points.
Rule: reduce the speed ratio to lowest terms a : b (here 8 : 5). Same direction → |a − b| distinct points; opposite directions → a + b points (13 is the trap for that case).
In 400 s A covers 3,200 m = 2 laps + 800 m. So successive meeting points are 800 m apart along the track: 0, 800, 400 (= 1600 − 1200), then 0 again.
Hence 3 distinct meeting points.
Rule: reduce the speed ratio to lowest terms a : b (here 8 : 5). Same direction → |a − b| distinct points; opposite directions → a + b points (13 is the trap for that case).
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