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 one 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 nth round to that for the previous round?

Let radius be 1 units and p = 3.14 or $$\pi$$ . So circumference is $$2*\pi$$.

According to given condition distance covered in first 1/2 mins = $$\pi$$/2 km, distance covered in next 1 min = $$\pi$$/2 km, distance covered in next 2 mins = $$\pi/2$$ km and finally distance covered in next 4 minutes = $$\pi/2$$ km.

Time taken to cover first round = 1/2 + 1 + 2 + 4 = 7.5 minutes.

Now time taken to cover $$\pi/2$$ is in GP.

For the second round the time taken is = 8+16+32+64 = 120

Ratio = 120/7.5 = 16