I just walked in the door from a 5K run, so I need to wait a few hours before I try the 30 second thing - I never time my pushups. I just did 33 to failure (ahem, right after the 5K run).
I do pushups almost every day, but I've gotten into short sets. On my TRX days, I will do TRX pushups at a couple of different angles and arm widths. I do two sets of each at 15-20 per set, so total 60-80 pushups per workout. I don't know if TRX pushups are easier or harder than regular pushups. I feel like I can do more arm-wise, but they work the hell out of my core, as you have to stay balanced so you don't fall on your ass. Certainly the TRX atomic pushups are harder. I used to do them, but haven't in a long while.
For regular pushups that I mix in with my yoga days, I'll use the perfect pushup contraptions and do three sets of 15 or two 15s and one 10, or just two 15s depending on how I feel. A few years back I used one of the "100 pushup" apps* and got up to 100, though it about killed me. Now at 59, I'm not sure if I could do it again. I know I can do 100 pushups in a day (I often "drop and do 10" just for kicks throughout a day) but I don't think I could do it in the 100 pushup timeframe (I think around 15min with rest breaks) anymore.
Age is hell on old guy muscles. It's all I can do to maintain muscle mass anymore, let alone build it. I'm using MP Combat powder almost every day just to keep up the protein. Depending on the study, old farts need around double the daily protein intake of younger guys just to stop muscle deterioration. That's actually hard for me to do - even being a big meat eater - without the help of protein powder.
* I will say, for anyone, even if you can only do 10 pushups, the 100 pushup app is a good way to increase your pushups. You don't have to follow it to 100. There are several levels, and you can start out with the "I'm a hefalump on the couch" level, which has you doing like 5 pushups, rest, 3 pushups, rest, 4 pushups, stop. Then you rest a day and do it again. It very slowly builds your endurance, so even if you don't wanna get anywhere near 100 pushups, it's a good way to get to 20.