A and B take round of a circular path of radius 70 m in opposite directions…
2018
A and B take round of a circular path of radius 70 m in opposite directions starting from a point O. When B reaches the starting point O the first time, he meets A there the third time (other than starting point). What is the ratio of speeds of A and B?
- A.
2 : 1
- B.
3 : 1
- C.
4 : 1
- D.
9 : 4
Attempted by 7 students.
Show answer & explanation
Correct answer: A
Concept: On a circular track, if two people start together and move in opposite directions, they meet again every time their combined distance covered equals one full circumference C. So the k-th meeting after the start happens when the combined distance travelled equals k × C, and a runner is back at the starting point exactly when their own distance travelled is a whole-number multiple of C.
Application: Let C be the circumference. The meeting described is the 3rd meeting after the start, so at that instant the combined distance covered by A and B is 3C. The problem also states that this same instant is the first time B reaches O, so B's own distance at that instant must be exactly one full lap, i.e. C. Hence A's distance at that instant is 3C − C = 2C. Since both travel for the same time, the ratio of speeds equals the ratio of distances: vA : vB = 2C : C = 2 : 1.
Cross-check: Take speeds in units vA = 2, vB = 1 (so vA + vB = 3 units). Meetings occur when the combined distance reaches C, 2C, 3C, … . At the 3rd meeting, B has covered (1/3) × 3C = C — exactly one full lap — confirming B is at O for the first time exactly at the 3rd meeting. This matches the given condition, so 2 : 1 is confirmed.