Let's do this question.
There is a square shaped running track of cyto kilometer inside the square.
There is a circular track inscribed inside the circle.
There is a regular hexagon shaped track inscribed and inside the hexagon there is a regular triangle
inscribed.
Now, remember, a regular triangle is an equilateral triangle.
Now for runners running around each track at the same speed, find the ratio of time taken by the forerunners
to complete one round.
All right.
Now pause the video, give it a try and then let's do it together.
All right.
Let's do it together.
Now, over here.
There are four persons and we need to find the ratio of the time taken by these four people to each
complete one round.
All right.
Now, over here, it's given that there is a square inside the square that is a circle inside the circle.
There is a regular hexagon and inside the regular hexagon, there is an equilateral triangle.
All right.
Now we need to find the ratio of the time taken by each person.
So let it be running around the square vs running a circular track, sees running a hexagonal track
and running the equilateral triangle track.
Now speed is equal distance by time.
Now distant time is equal distance by speed.
Right.
You take time over here and take speed to the right side so you get time is equal distance by speed.
Now you can see that time is directly proportional to distance when speed is constant.
Now, over here, it is mentioned that these four guys are running at the same speed.
So therefore time is directly proportional to the distance.
That means the time taken by E will be proportional to the distance that it needs to cover.
And it's mentioned that everybody completes one round.
Right.
All right.
So what would be the time taken by it to complete one round?
It's given that the side of the square is two kilometers.
So the distance that he has to cover is four and the two right perimeter of a square is four in the
side.
So if time is proportional to distance, I can see that time taken by is equal to can do for three or
for in to ride Gaiser constant.
Now what about time taken by B it will be gain to distance that B has to travel.
B has to travel a distance of poopy into one.
Right.
This is equal to two km.
Therefore radius of the circle will be one kilometer.
Right.
Therefore time taken by Biscayne or to buy into one part of our time taken by sea.
We have seen that the side C can be found as a two.
Right.
Where is the site of the square where it's given that it's two km.
So site of this hexagon will be two by two.
That's equal to one.
Therefore, the perimeter of this hexagon will be six, right?
Six and one that's six.
Therefore, time taken by C will be gained to six.
And what about the time taken by the person who's running the equilateral triangle track that would
be gained to three three.
Right.
And therefore the ratio of the time taken by these four people will be boring to do is to two.
Pi is to six is to three route three.
That is the answer to this question.