A length of path ACB is $$1500$$ m and the length of the path ADB is $$2100$$ m. Two particles start from point A simultaneously around the track ACBDA. One of them travels the track in clockwise sense and other in anticlockwise sense with their respective constant speeds. After $$12$$ s from the start, the first time they meet at the point B. After minimum time (in$$ $$s) in which they meet first at point B, will they again meet at the point B is time $$tmin=(12)xs$$. The value of x is $$__________$$

Question

A length of path ACB is $$1500$$ m and the length of the path ADB is $$2100$$ m. Two particles start from point A simultaneously around the track ACBDA. One of them travels the track in clockwise sense and other in anticlockwise sense with their respective constant speeds. After $$12$$ s from the start, the first time they meet at the point B. After minimum time (in$$ $$s) in which they meet first at point B, will they again meet at the point B is time $$tmin=(12)xs$$. The value of x is $$__________$$

Infinity Learn · Accepted Answer

The velocity of first particle is $$v1=150012ms$$−$$1$$ and the velocity  of second particle is $$v2=210012ms$$−$$1$$. Let after completing $$n1and$$ $$n2$$ trips, they will again meet at the point B.∴ $$(1500+2100)n1v1=(1500+2100)n2v2=t$$ Or  $$n1n2=v1v2=150012210012=15002100=57$$∴ $$tmin=3600$$×$$5v1=3600$$×$$51500$$×$$12=144s=(12)x$$∴ $$x=2$$

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