Two cyclists start on a circular track from a given point but in opposite…

Concept: When two bodies move in opposite directions around a closed circular track, starting from the same point, the gap between them closes at the sum of their speeds (their relative/closing speed). They are together again for the first time as soon as their combined distance covered equals the length of the track once.

1. Let the two cyclists' speeds be 7 m/sec and 8 m/sec. Since they move in opposite directions, their closing speed is the sum: 7 + 8 = 15 m/sec.

2. The track's circumference is 300 m. For two bodies moving toward each other on a loop, they meet for the first time once their combined coverage equals this circumference once.

3. Time to meet = circumference ÷ closing speed = 300 ÷ 15 = 20 seconds.

Cross-check: In 20 seconds, the first cyclist covers 7 × 20 = 140 m and the second covers 8 × 20 = 160 m. Together that is 140 + 160 = 300 m — exactly one circumference — confirming they meet at the 20-second mark.

Note on wording: this question is commonly phrased as meeting "at the starting point"; the standard convention for this widely used problem treats it as the cyclists' first meeting anywhere on the loop (computed by the combined-speed method above), not a simultaneous return of both cyclists to the exact starting point together (which would use the LCM of each cyclist's own lap time and gives a different, larger value).