Decreasing number of push-ups

The primary issue here is almost certainly insufficient rest. You have begun with a nominal volume and are working toward higher intensity. But our tolerance to volume is entirely a function of our conditioning, so straight away—unless, of course, you were already very well conditioned—you have begun with a workload that is in excess of your ability to recover and adapt.

To put this into perspective, it is akin to preparing for a marathon by running 42.2 kilometres (26.2 miles) every day. Needless to say, such an approach would be untenable.

A better approach is to perform a volume from which you can recover in a day, then gradually increase that volume. If you are performing your sets to failure, that is likely just one set—and whatever number of repetitions that amounts to. (Record them!) Alternatively, you might prefer to do a nominal number of sub-maximal sets and repetitions. Two sets of 15, for example, would represent more volume and practice, but would likely result in comparable stimulus and fatigue.

As your condition improves, you will be able to tolerate a higher volume of work. However, for better multilateral development, you should not limit yourself to modifying volume alone. You will benefit more by changing the other variables too—in particular tempo and type. Slowing down your repetitions will increase time under tension; speeding up your repetitions will increase peak force output for the same load, which in this case is limited by your body weight. Push-ups can further be modified by changing the position of the hands (wide, narrow, Ace-of-Spades, et cetera) which, in turn, changes muscular recruitment significantly. So too changing the elevation of the feet and the depth of push-up (shallow, floor, between chairs, et cetera).

If your objective is not to be a push-up specialist, but rather to develop your physique, varying your choice of exercises will be far more effective than simply increasing your repetitions.

I hope that adds something to the discussion.

Unlike what the user Andy says

It was been shown that there is no difference in hypertrophy when comparing high lod training to low load and high repetitions training.

Apparently even 30% of 1 RM is enough to build muscle which translates to roughly the 100s and above rep range.

So do not worry, you don't need to use books or buy weights, even when you will reach the point of doing 100 push ups in one single set. You will still build muscle.

Also as suggested by Mike Israetel, 3 sets of chest training a week are barely enough to maintain size...not even remotely enough to build muscle.

20 reps mainly build muscular endurance not muscle mass. For muscle mass you should be in the 5-12 rep range. So you need to increase the difficulty of the push-ups somehow. You could try doing push-ups with an elastic resistance band or a backpack with some books in it on your back. You could also try elevating your feet slightly. Do not go completely to failure except for on the last set.

If you can do dips, a combination of dips and push-ups may also be an option. Dips are heavier than push-ups. You could for instance do 1 set of push-ups followed by two sets of dips followed by one set of push-ups.

You should do pull exercises at least as much as you push. Regarding the pull-ups you will need to start with a simpler version so I think you should lower the bar to ca. 1 meter above ground and do australian pullups (inverted rows): https://www.youtube.com/watch?v=tB3X4TjTIes. If moving the bar is impractical you could attach suspension trainer (TRX) cords to it. With these you can also do facepulls, which are really good for the shoulders.

It is really important that you initiate any pulling movement by pulling your shoulderblades together and down: https://www.youtube.com/watch?v=ixd8Aib5ZPc Do not increase weight faster than you can manage this. You may be able to move more weight by using mostly biceps but this will lead to a muscular imbalance that causes forward rounded shoulders. For the same reason it is a good idea to alternate between horizontal (australian pull-ups are horizontal) and vertical pulling (it is easier to engage the muscles pulling your shoulderblades together and down with horizontal pulls).

Also occasionally do some wall angels.

Also you should not train the same muscles every day. Muscles need rest to grow. And the older we get the more rest they need. You should cut it down to 3 days a week or every other day. 3-4 sets of push-ups per workout are probably enough.

I've answered a similar question that covers some of the same points: My pushups don't increase

Why you're not progressing

If you're wondering why you're not progressing here, it's because you're doing the same thing over and over. Your body simply adapts to doing just that, and doesn't get challenged. Imagine trying to learn math by solving 5+7 over and over. At some point, we're just repeating a routine rather than actually working to figure things out. The challenge is gone, and with it goes our chance to progress to the next level.

What's missing

There's a lot more than just the actual working out that goes into improving your performance. The big trifecta we usually preach is

• the workout

• the diet

• the sleep

You can't focus on two out of three here, and expect results. It needs to be all three.

Since there are some details missing with regards to the quality of your diet and sleep, I will forego that for now, and focus on the training. But keep in mind that none of these tips will serve you unless you eat well, and sleep well. If at any point you feel more fatigued than you've used to, a reduced quality of eating and sleeping habits are the usual suspects.

Neglecting the bigger picture

A common mistake is to look in the mirror, find a point you want to work on, and focusing exclusively on that. You mention you want to get some bulk on your arms by November, and I'd say that's doable. But if you only work out your upper body, this has a tendency to cause imbalances in your body, which leads to back pain, neck pain, hip pain, and from there it just branches out.

Since you have a short-term goal in mind (some arm bulk with a 4 month timeframe), I'd say it's fine to concentrate more on the upper body, so long as that's not a permanent thing.

How to start progressing again

Here's what I'd recommend:

• Pushups are good, but stop focusing on increasing the number of repetitions, and find a way to add some weight to it. Rather than doing 20 reps per set, find a weight that limits you to 8-10 reps per set. It could be in the form of someone placing some light weight on your back, or you could find a weighted vest that allows you to adjust the weight.

• Definitely continue trying to do pullups or chinups. If you focus only on pushing exercises, and too little on pulling exercises, we're once again concerned about muscular imbalances, this time in the shoulder/neck region.

• Add at least one exercise for your legs to your routine. I would suggest reverse lunges, and also here, if you find yourself being able to do dozens of repetitions, start challenging yourself to holding some weight in your hands.

Age

I suppose there is a point to be made about seeking progress in an advanced age, but 62 isn't too old to get in shape and look good. But keep in mind that any and all pain should be scrutinized, preferably with the consultation of a doctor or a physical therapist. That goes for all ages, but it becomes more important with every birthday.

Realistically speaking we do not know enough about you to judge...it could be just mental or maybe you didn't sleep or eat right this week.

Some may say you need to rest every other day, but I don't think 100 push ups are enough stress that force you to need a rest day.

If your goal is to do 100 push ups in a day, use a 10 second interval timer and do 1 of up to 20 push ups every 10 seconds. I suggest starting with 1 push up every 10 seconds and progressing by adding more reps through the interval.

1 push up every 10 seconds takes about 16 minutes to complete.

This is a nice warm up or morning routine to wake up, but unless you are a completely beginner who never did any sport in their life, don't expect to grow any muscle from such little work.

Here is an interval timer of 10 seconds on YouTube if you need it or otherwise download an app from the play store or app store.

https://youtu.be/Xjv2-F6Quls