My late MIL was often heard referring to (for example) "getting delayed by old people" (they did a few coach holidays per year). She was in her early 80s then (but still quite lively and agile) and when FIL pointed out "aren't you old too?" got a "certainly not" fired back!
The first time someone offered me a seat on the Tube (we only visit London occasionally) I had to resist the temptation to say "No thanks -- do I look old" as I just about realised in time that the obvious and uncomfortable answer was "well, um, yes".
Now if shop assistants make comments about being old (I don't look frail or doddery, at least, I don't think so . . .) I try and make some little joke about easily forgetting things, perhaps.
If I get an "aw, bless" from them, as someone said, I have to resist the temptation to get cross!