Problem #PRU-5062

Problem

Eleven people were waiting in line in the rain, each holding an umbrella. They stood closely together, so that the umbrellas of the neighbouring people were touching (see the figure)

The rain stopped and everyone closed their umbrellas. They then shuffled closer, keeping a distance of \(50\) cm between neighbours. What is the ratio of the old queue length to the new queue length? People can be considered points, and umbrellas are circles with a radius of \(50\) cm.