since the two particles collide(in electrostatic sense), so applying cons. of linear momentum, when the two particles acquire zero relative velocity, v=u/2(from com).let minimum seperation be x, decrease in ke=increase in epe. kQ1Q2/x-kQ1Q2/d (where d is initial distance b/w them, in this case probably infinity)=1/2*m*u^2-1/2*m*(v^2)*2, now solve to get the answer. this was min seperation , for common velocity we can also try thinking that the particle x will continue to move towards Y with decreasing speed, while y will move with increasing speed this means that the seperation keeps on decreasing, after some time when v relative is zero only then minimum seperation occours