Question: A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is πr during the first 30 seconds, πr/2 during next one minute, πr/4 during next 2 minutes, πr/8 during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round?
Let πr = x.
∴ The circumference of the circular path = 2x.
∴ The sprinter covers 2x metres in one round. The time taken to complete each round is as under:
Thus, we see that the ratio of time taken for the second round to that for the 1st round = 16.
Similarly, ratio of time taken for the third round to that for the 2nd round = 16 and so on.
Hence, option (c).