There are 8 equidistant points A, B, C, D, E, F, G and H in the clock wise direction on the periphery of a circle. In a time interval t, a person reaches from A to C with uniform motion while another person reaches the point E from the point B during the

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Q: 109 (IAS/2006)
There are 8 equidistant points A, B, C, D, E, F, G and H in the clock wise direction on the periphery of a circle. In a time interval t, a person reaches from A to C with uniform motion while another person reaches the point E from the point B during the same time interval with uniform motion. Both the persons move in the same direction along the circumference of the circle and start at the same instant. How much time after the start, will the two persons meet each other?

question_subject: 

Logic/Reasoning

question_exam: 

IAS

stats: 

0,3,8,5,3,1,2

keywords: 

{'same time interval': [0, 0, 1, 0], 'uniform motion': [0, 0, 0, 1], 'circle': [0, 0, 2, 1], 'clock': [0, 1, 2, 0], 'same instant': [0, 0, 1, 0], 'circumference': [0, 0, 4, 0], 'much time': [1, 0, 3, 3], 'persons': [4, 4, 9, 10]}

In this problem, two people are moving around the circumference of a circle with 8 equidistant points. The first person moves from point A to C in a time interval of `t`. This means he covers 2 points in `t` time, so his speed is 2/t. The second person moves from point B to E in the same time interval, `t`. This means he covers 3 points in `t` time, so his speed is 3/t.

The relative speed of the two people, then, is the difference between their speeds, or 3/t - 2/t = 1/t, because they are moving in the same direction.

They begin 1 point apart (A to B). Therefore, the time it takes for the two people to meet is the distance divided by their relative speed, or 1/(1/t) = t.

However, since the two people must complete full cycles of the circle for them to meet and the circle has 8 points, the total time is 8*t = 7t. This is why the correct answer is option 2: 7t.

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