Ranks

Let's consider the scenario of an army:

Say, a soldier joins the army as an Lieutenant (少尉). If he passes the promotion board examination, he will be become a Captain (上尉) 3 years later. After another 4 years, if his performance is reasonable, he will be advanced to be a Major (少校). With another 5 years, if nothing goes (seriously) wrong, he will be appointed as a Colonel (上校). Further promotion to a General (將軍) is more tricky and depends on a lot of political factors.

The mathematical question is: How many officers should there be in each rank?

There are actually two aspects of this question. The more simple consideration (but with a wider implication) is to divide the officers into junior (Major or below) and senior (Colonel or above) ranks. If soldiers graduate from the military school at the age of 25, they will become Colonels at the age of 37. If the age of retirement is 60 and no one leave this system prematurely, the inevitable consequence predicted by simple arithmetic is the senior-to-junior ratio of this system is two-to-one.