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Question

A,B,C and D participate in a cycling race on a circular track such that they are 100 m. 120 m, 110 m and 105 m away from the center of the circular track. Their speeds are 48 m/s, 40 m/s, 42 m/s and 44 m/s respectively. If their starting positions are collinear with the center of the track, which two players will have to change their positions so that both of them will complete two rounds of the circular track simultaneously? 
  1. A and D
  2. A and C
  3. C and D
  4. A and B
  5. either (b) or (c)


Solution

The correct option is A A and D

Option (e)

If A and B interchange positions, time taken by A = 120/48 seconds and time taken by B= 100/40 . Hence A and B have to interchange their positions

Also to achieve a dead heat if C and D interchange their positions, time taken by C and D

is 105/42 and 110/44 . Hence, C and D can also change their positions to arrive at a dead heat.

However, If A and D interchange positions, dead heat will not be achieved.

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