How long for Google to de-index bad pages?

I've been setting up a new site of mine and I forgot to add noindex to certain pages: privacy policy, category pages, tag pages etc as well as a bunch of pages I was doing some testing on which I don't want indexed/visible.

So at the moment I have about 40 pages indexed in the SERPS, when really it should be about 20 (my good pages). Over a week ago I added noindex to all the bad pages, but they're still showing up when I search for my site like site:mywebsite.com

Does anyone know how long it should take for them to disappear?

weeks or even months
use *remove pages tool* in GWT to remove them instantly