how to go up in ranks the fastest?

The algorithm is quite unknown which makes it seem random. I say try and reach the highest score you can by top fragging as well as planting whenever you can (planting gives you some added score). I think ranking up isn't just about getting the kills, it's also about being dynamic, even in terms of map picking. So don't stick with one map, play 3-4 maps when you join matchmaking.