A and B walk around a circular track they start at 8 am from the same point in opposite directions A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9:30 am?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Concept: In this question, A's relative velocity to B is 5 laps per hour. This will cause A to cross B five times an hour. Therefore, calculate the time from 8 am to 9:30 am and apply a consistent method to get the total number of intersections within that time frame.
Given, Walk at a speed of 2 laps an hour. And B goes at a speed of 3 rounds an hour. But given that they are moving in the opposite direction from the same point. Therefore, the relative speed of A and B is

laps per hour (the "+" sign is in the opposite direction when moving in the same direction as the "-" sign is displayed. Because it is moving.) This means that A and B intersect 5 times an hour.
Now, given that they start at 8am, we need to find out how many times they will cross by 9:30 am (i.e. within 1. 5 hours). That is, it crosses 5 times in an hour, so it crosses at least 2 times in 30 minutes (because 2. 5 is not possible and 3 cannot be taken). Therefore, in an hour and a half, they intersect each other

Therefore, it will cross 7 times by 9:30 am.
Hence, the correct answer is option (2).

Watch 3-min video & get full concept clarity