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A sprinter starts running on a circular path of radius $r$ metres. Her average speed (in metres/minute) is $\pi r$ during the first $30$ seconds, $\pi r /2$ during next $1$ minute, $\pi r /4$ during next $2$ minutes, $\pi r/8$ during next $4$ minutes, and so on. What is the ratio of the time taken for the $n$-th round to that for the previous round?

  1. $4$
  2. $8$
  3. $16$
  4. $32$


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