In the story "The Most Dangerous Game," how old is Rainsford?
The answer to your question is "the book doesn't say." That is a very unsatisfying answer, isn't it? There are ways around it, though. The text implies certain things about Rainsford, and from them we can arrive at what is probably a good guess at the man's age.
Most telling is when the General says: "Dear me, what a righteous young man you are!" So what does this mean? Well, according to Rainsford, the General is "past middle age, for his hair was a vivid white..." So the question here is "what would the General consider 'young?' During the time frame of the story, I would suppose that middle age came a little earlier than it does today, probably in the early to mid 40's (unlike the later forties, early fifties we might think of today.) He has white hair, but is still fit enough for physical activity, so I would guess the General is somewhere in his 50's.
By that standard, I would guess that "young man" would refer to someone in their 20's or 30's (maybe early 40's.) I favor 30's, personally. Rainsford is reported to be a great hunter of some renown. This would be unlikely for someone to achieve in their 20's. In addition, the General mentions the books that Rainsford has written on the subject. This implies a more mature, experienced mind. And while I know that a man in his 40's that is in good shape can still be very athletic, the amount of swimming and running that Rainsford does implies someone has a lot of stamina. I'm not saying that someone in their 40's wouldn't have that, just that someone in their 30's more likely would.
So that's my guess: mid thirties.