Hi, in this session we will be learning the concepts of Circular Races. Now what really is a difference

between Linear and Circular Races apart from the fact that one is a straight line and the other one is

a circle. Well, there is one more difference and that is in a Circular Race there is a possibility that the

two runners will keep meeting again and again. Didn’t understand? Let’s see a circular track and the

two people are starting the race, something like this, tell me when will the faster runner B once

again meet A. When will the two of them meet for the first time? If you realise here, right, they have

met once again, and did you realise that in this case the faster runner has taken a lead of one full lap.

One full circumference over the slower runner A. Didn’t understand? Let’s put some values you will

understand. Right, if you realise A has completed only quarter of a circumference, that is quarter of

a circle, whereas B has completed one full round, one full circle and another quarter, one quarter.

So did you realise that A has taken a lead of one full lap over the slower runner. Right, B has taken a

one full lap lead over the slower runner. So when will they meet for the first time, when the faster

runner takes a lead of one lap over the slower runner. In this case slower runner is A. Right, and

now that they have met here we can always assume that this is the fresh race starting and hence

every subsequent meeting will happen at multiples of these values. Which means, if I assume that

the race starts here they would now meet another quarter of a circle in clockwise direction from this

point. So the second meeting will happen here, where A has completed half a lap and B has

completed two full laps and another half a lap and hence the lead now is two, right. Okay, the third

meeting hence would happen here when A has completed three quarter of a lap and B has

completed three full laps and another three quarters. The lead is three laps. And finally they would

meet again at the starting point. Because A would have now completed one full lap and B would

have completed his fifth lap, right. And now the lead between them is four laps as you can see

there, right, which means they will come back at this starting point for the fourth time, their fourth

meeting. Now how would you put them in perspective, right? If you realise the ratio of their speeds

is 1 is to 5. How did we find that? Well, for every 1 lap that A covers B has covered 5 laps. So it is

obvious that the ratio of their speeds is 1 is to 5. And since they were running in the same direction

the difference in these parts 1 and 5 is 4. So there are two things that we should know, one they will

meet at four points along the circumference, right, as you can see that they would have met at four

points at every ninety degrees distance. Secondly their fourth meeting will happen back at the

starting point, right, just remember this, four meet points and fourth meeting, right. Now let’s see

what happens if they were to travel in opposite directions, something like this, right, now tell me

when the two of them will meet for the first time. Look at this they are travelling at the opposite

direction, and now you would realise that they have met here for the first time and in this case

together they have completed one full lap, right. If you see A has covered that much distance in

anticlockwise direction whereas B has covered the remaining distance in clockwise direction,

together they have managed to complete one full lap. So in opposite direction the two of them will

keep meeting the moment they complete one-one full laps together, right. The first meeting would

happen when they complete one full lap.