More along the lines of :
The Doc keep the same face for 200 Years ?!?! 
He's an alien.
If the Doctor ages physically in conventional terms (and there's no mention that he does) then it's at a much slower rate than humans. I know he was meant to have been in the Patrick Troughton form for around 60 years - he looked like he was in his mid fifties when he first appeared in that form but I wouldn't have said he looked 115 in his last appearance.
All that being said, we don't know if he gives his age in Earth or Galifreyan years (or both on and off) and how would he actually measure how many years have passed when he's travelling through time rather than being on an actual planet? Also, he's said once before that the interior of the Tardis is "outside of time" meaning even a human like Amy could travel around in it for thousands of years and not noticeably age (providing she didn't spend much time out of it).
