fapel said:how long should it take to go from doing 7 pullups max to 20 pullups?
Impossible to say. It took me about 7.5 months to go from doing 9 pull ups to 23, but that was one of my main goals in preparation for BUD/S class 245. I was in boot camp for 2 of those months and that didn't help, but didn't hurt either. Kind of stalled a bit... no pull ups in the Navy boot camp. Had to sneak them in after hours on doorframes in the bathroom. Not super comfortable on the hands. I was eating everything, and lots of it.
May as well ask how long it takes to save 200 dollars... everyone will give you a different answer and none might apply to you. Eat well, train regularly, and see where it takes you.