Let the final relative velocity of B wrt A, when it crosses A, be: v′.
It is given initial relative velocity of B wrt A is: 0−V=−V
Initial relative displacement and final relative displacement is 0 as the particles are at the same position initially and finally. Hence, total relative displacement of B wrt A is 0.
From third equation of motion,
v2f=v2i+2as
v′2=V2
v′=±V
As seen before, −V corresponds to the initial relative velocity.
Hence, +V corresponds to final relative velocity.