In OBR a balk is a delayed dead ball situation. If as a result of the pitch, every runner AND the batter advance at least one base then the balk is ignored. Otherwise the pitch is ignored and the balk enforced.
So in your situation, the balk would be ignored because R1 advanced at least to second AND the batter safely reached first.
From what I've seen on this website I believe using the FED rulebook a balk is an immediate deadball situation, so the runner would be advanced to second and the batter remains at the plate.
Difference in rulebooks:
OBR: "That's a balk!.....wait for play to end..(if all runners don't advance at least one base or batter doesn't reach first) TIME!!!!"
FED: "TIME!! That's a balk!"
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