Question

In a certain country, there are more than 101 cities. The capital is connected by flight routes to 100 cities, and every city other than the capital is connected by flight routes to exactly 10 cities. It is given that from any city, it is possible to reach any other city (possibly not by a direct route). Prove that it is possible to close half of the flight routes leading to the capital such that the possibility of reaching any city from any other city is preserved.