The Gemara, starting in Megillah 27b, starts describing various situations where different sages were asked how they merited to reach a long life. Presumably, this was because, at the time they were asked, they were considered to be 'old'. Do any of the sources discuss how old they were when they were asked (or alternatively, when they passed away)?
Based on this handy chart from Wikipedia, average life expectancy from those times seemed to be in the 20-50 range, so does that mean someone in their 60's would be considered 'having merited old age'? On the other hand, there are the numbers found in biblical sources (which weren't that far back from those days...) and I seem to recall various midrashim speaking about Amoraim in the few-hundred-year range, so that would imply at least 100+ years for for someone to be notably old.