We call the point where A & B start: Zero point ( 0 point), the point "x" meters away from "0" point in the direction that A & B move : the point x.

Speed discrepancy between A & B : 400 - 250 = 150
If A & B meet, A must move faster than B a distance that is the multiple of 100m ( a fulll circle)
the first time they meet is after : 100/150 = 2/3 hour, the position of the point: 2/3 * 250 = 166.66 m or at point 66.6
the second time they meet is after another 2/3 hour , the position of the point: (2/3) * 2 * 250 = 333.3 or at point 33.3
the third time they meet is 2/3 hour after their second meet, the position of the point: (2/3) * 3 * 250 = 500 or at point "0"
Now we get the rule: the forth point will be at point 66.6, the fifth: point 33.3, the sixth: point zero, and so on.
So there're only three positions that A & B will meet

This is the rule that I figure out ( IMO only, not from any official sources) :
Circle length : 100
Speed discrepancy : 150
time between each meets: 100/150 = 2/3 ( note that you must simplify the fraction as much as possible, for instance 6/15 must be changed to 2/5)
the number of points is the smallest positive integer that multiplies to "2/3" will give out an integer. This case is 3
Take another example:
A's speed : 500
B's speed: 200
Circle's length: 400
Speed Discrepancy: 300
Time period: 400/300 = 4/3
No. of points A & B will meet : 3 ( as 3 is the smallest positive integer that multiplies to 4/3 to give out an integer)

Awesome technique suggested by Limestone . Though, there has been a mistake in the example suggested , it should be 400/300 or 4/3 , in which case the answer will be 3. Nevertheless, I guess the mistake was due to oversight and hence the technique still remains awesome . Thanks !!

I wasted more than half an hour and then i realize that its good to look at the answer...

Thanks Limestone for putting such a brilliant technique, but one thing i need to ask in the

the first time they meet is after : 100/150 = 2/3 hour, the position of the point: 2/3 * 250 = 166.66 m or at point 66.6

why 250 what is the source of this 250, why not 150 ...
Please explain.

goyalsau wrote:I wasted more than half an hour and then i realize that its good to look at the answer...

Thanks Limestone for putting such a brilliant technique, but one thing i need to ask in the

the first time they meet is after : 100/150 = 2/3 hour, the position of the point: 2/3 * 250 = 166.66 m or at point 66.6

why 250 what is the source of this 250, why not 150 ...
Please explain.

Now, since time is constant or same for both , and since the faster person will take a lead from te begining , he will meet the slower person only after covering the length of the circumference of the circular track. Hence, the slower person will always be lagging behind and by the time the slower person covers the length of the track for the first time the faster person may have covered the length of the track multiple times . So, the meeting point on the track is determined by the speed of the slower person, which is 250 in this case. I hope this clarify , but I would appreciate if Limestone or anybody else has a better explanation.

Thanks Aman verma for spotting my mistake.

2/3 hour is the time for A & B to meet after they start. I want to locate where they will meet in the circle, so I must calculate the distance A will have gone after 2/3 hour ( you can use that of B as well. It will give out the same result as A & B are at the same point after 2/3 hour)
Using A: 250 (the speed of A) * 2/3 = 166.6 or we can say 100 + 66.6
Using B: 400 (the speed of B) * 2/3 = 266.6 or we can say 200 + 66.6
We can see here B has gone 1 round faster than A after 2/3 hour.

150 is the speed discrepancy between A & B. It is only used to calculate how long it will take B to go more than A one round.