Need an advice from a pro

Hi all,

I am 46 years old. I try to eat healthy and exercise 3 times a week (175, 5-10, size 31, very lean). Although I am in good shape and has been going to gym for years, I don't consider myself knowledgeable when it comes to training. So I have a questions for those who are more knowledgeable.

I usually do 3 sets of 10-12 reps of each exercise. But I see people doing one set of 10-12 rep of a specific exercise, then move to another exercise and do one set, then move to another one and do one set, and then move back to the first one and do one set....(i.e one set of bicep, one set of chest, one set of shoulder, then another one set of bicep, one set of chest, one set of shoulder, .....). The obvious advantage of this method is time saving since you can reduce the rest between sets since you work on different muscle groups.

This is my question : is this a smart way of working out when you have limited time to work out? Does it increase/decrease the result? Do it or don't do it?

Thanks in advance:)

Need an advice from a pro