How much horsepower does a arctic cat 250 2x4 atv have that has been bored 40 thousands over ?

 

These aren't race bikes. I would be more concerned that you get the carburetor spot on. Arctic Cat's are a bit conservative, but generally they tend to last. I just sold a 2001 AC 500 with 9,000 miles. It had a race cam, K&N, 5 degree timing advance key, free flowing exhaust. Running 93 octane, on a Mustang dyno, it put down 29.5 rwhp. Crank hp, maybe 38-39. You have half the displacement, doubt if you have more than 20 hp, just a wild guess.