You're get a roll number, you write a test, a list gets published that ranks all the roll numbers, sometimes with scores. Colleges offer admissions to anyone who scored between ranks 1-N. At more elite schools N is small (e.g. 100), but in lower ranking schools N is large (e.g. 100000+).

Affirmative action is practiced by having different Ns for different disadvantaged groups (i.e if you are a lower caste, N=1000, but for general admissions, N=100)

The downsides of this system are that it still fails to eliminate economic biases (i.e a student from a well to do family can hire tutors who help them test prep better) and that it's impossible for the school to control the makeup of a class - e.g in a year I was in school, a new test prep school opened up in a city and students from that school scored significantly higher than others in the admissions test. So, about 50% of the incoming class were students who went to that test prep school.