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Let's do this question.

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There is a square shaped running track of cyto kilometer inside the square.

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There is a circular track inscribed inside the circle.

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There is a regular hexagon shaped track inscribed and inside the hexagon there is a regular triangle

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inscribed.

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Now, remember, a regular triangle is an equilateral triangle.

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Now for runners running around each track at the same speed, find the ratio of time taken by the forerunners

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to complete one round.

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All right.

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Now pause the video, give it a try and then let's do it together.

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All right.

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Let's do it together.

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Now, over here.

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There are four persons and we need to find the ratio of the time taken by these four people to each

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complete one round.

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All right.

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Now, over here, it's given that there is a square inside the square that is a circle inside the circle.

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There is a regular hexagon and inside the regular hexagon, there is an equilateral triangle.

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All right.

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Now we need to find the ratio of the time taken by each person.

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So let it be running around the square vs running a circular track, sees running a hexagonal track

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and running the equilateral triangle track.

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Now speed is equal distance by time.

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Now distant time is equal distance by speed.

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Right.

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You take time over here and take speed to the right side so you get time is equal distance by speed.

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Now you can see that time is directly proportional to distance when speed is constant.

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Now, over here, it is mentioned that these four guys are running at the same speed.

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So therefore time is directly proportional to the distance.

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That means the time taken by E will be proportional to the distance that it needs to cover.

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And it's mentioned that everybody completes one round.

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Right.

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All right.

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So what would be the time taken by it to complete one round?

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It's given that the side of the square is two kilometers.

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So the distance that he has to cover is four and the two right perimeter of a square is four in the

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side.

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So if time is proportional to distance, I can see that time taken by is equal to can do for three or

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for in to ride Gaiser constant.

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Now what about time taken by B it will be gain to distance that B has to travel.

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B has to travel a distance of poopy into one.

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Right.

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This is equal to two km.

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Therefore radius of the circle will be one kilometer.

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Right.

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Therefore time taken by Biscayne or to buy into one part of our time taken by sea.

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We have seen that the side C can be found as a two.

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Right.

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Where is the site of the square where it's given that it's two km.

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So site of this hexagon will be two by two.

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That's equal to one.

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Therefore, the perimeter of this hexagon will be six, right?

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Six and one that's six.

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Therefore, time taken by C will be gained to six.

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And what about the time taken by the person who's running the equilateral triangle track that would

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be gained to three three.

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Right.

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And therefore the ratio of the time taken by these four people will be boring to do is to two.

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Pi is to six is to three route three.

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That is the answer to this question.