At my peak I was able to do forty push ups. That was twenty years ago and although I can produce twenty now with no training, any more is a struggle.
Colleague at work just told me he regularly does 100, sometimes 300 push ups.
After I picked my jaw off the floor I asked his secret. Turns out he cheats... Not really, but I used to think if you stop and rest that its cheating.
In reality it's just a different technique.
Sets of ten or twenty with a short break in between. The break gives your muscles a chance to recover but not too long to allow you to get pumped.
I haven't tried this yet but am going to give it a shot. It should work equally well with pull ups and sit ups.
Managed a 7K run this morning. Time was slow but felt good to complete it.