how to improve pushup/pullup numbers

just do them a lot… mic it up and spread them though out the day… one you are really fatigued take a couple days off… just keep doing them.

The best way to improve on these things is to do a single set about every hour, hour and a half (full recovery) all day long.

Look up "Greasing the Groove" method

these exercises are just endurance exercises because they all bodyweight. best way to improve them is do as many as you possibly can in a week though making sure you have 1 - 2 days rest between each time you do it so i think alternative days is good. maybe youre already doing it but what i find helped is doing lots of very small sets with like 1.5 - 2 minutes rest or even more. maximises how many you can do in a day and week. longer sets will exhaust you and you end up doing less in a week.

You can train chin variants 3-4 times per week. If you are only doing 1-5 reps, then some absolute strength will help at first. Try weighted chins. Once you can do 10+ it is becoming an endurance exercise. Nevertheless, a little strength reserve can't hurt. Also switch up reps and recovery. You can do 8x5 with 30 secs rest for example, as opposed to 4x limit sets with longer rest.

This is an excellent pull-up program but it also has you do push-ups.

armstrongpullupprogram.com

The Armstrong Workout - Armstrong Pullup Program

Jump to Day 1 First…do you have a pullup bar? If you want to easily challenge yourself daily–get that piece of gear! If you need an easier start, try our Beginners workout here. If your pullups have plateaued, try the Advance...

Link:armstrongpullupprogram.com/

This is (obviously) a very productive schedule for you. Keep it, I would say.

As your numbers continue to climb you may find you need more recovery, perhaps simply to skip a day occasionally. That's fine.

Otherwise: Using sets is generally more productive than simply working till exhaustion on a given day. A random example: Working up to 10 sets of 10 pushups may stimulate more progress than doing a single set until you can't do any more. (I realize you may be using sets already.)

TL, DR: What you're doing seems to be working. No need to change.

You haven't told us your current training, other than you're alternating days. Whatever it is, it seems to be working for you because your 1 month improvement is great.

There's a plan out there called 100 pushups or 100 pushups challenge. I've tried it, but I keep getting shoulder injuries... I think because I have an old shoulder injury. IIRC, it's 5 sets of roughly 60% max reps with the 5th set being to exhaustion. For example, if you can do 40 now, it might be 25, 27, 25, 23, xx... with xx being more than 25. Anyway, you can look it up. Five years ago (age 69) I could do 74.

Why change what’s working? Regular practice with good form is all there is to it.

One day do pull ups at VO2 max pace. Another day longer pull up reps at 10 pace. Sundays is long pull up day. Easy pull ups the other days. Doubles are good.

Very smart!