Boo's age is never specifically mentioned by Harper Lee, but we can make an assumption. From the description of the trouble that Boo got into with his friends - the trouble that caused him to spend some time in the county jail - we can assume that Boo was a teenager at the time. Lee says after this that "he was not seen for fifteen years." This is because Boo's father, a devoutly and strictly religious man, kept Boo locked up in the house. Add 16 to 15 and you get 31. Boo's father has died and now his brother Nathan has moved in. This seems to be well-established. The kids know who Nathan is (and know to avoid him). Thus, we can assume when the story starts that Boo's dad has been dead at least a year or two.
From all this conjecture, I would suggest that Boo is in his 30s. It is important that Boo be clearly established as an adult, because it supports the theme of coming of age in this story. Boo himself - having been isolated - is just coming of age. Jem and Scout each have moments of coming of age, just as the town itself does. What this proves is that "maturity" isn't about age as much as it is about experience and about becoming more tolerant of the world around you.