Well there would be more A particle for B to collide and react with so the overall reaction would be faster.
Imagine it like this, in one scenario there were 50 girls and an excess of boys walking around in one room and in the other there were 25 girls and an excess of boys walking around in one room. In both scenarios, the room size is the same so in which one would it be more likely for a boy to walk into, or collide with a girl?