Two insulated charged copper spheres A and B of identical size have charges qA and qB respectively.When they are brought in contact with each other and finally separated, what are the new charges on them?

Here after the contact ,both the surfaces of the sphere will have the same potential .so,

assume that q(a) > q(b)

let x be the charge lost by sphere A and which is gained by sphere B

K(q(a)-x)/r^{2 =}  K(q(b)+x)/r²       

q(a)-x=q(b)+x

[q(a)-q(b)]/2=x

the new charge on,

SPHERE A = q(a) -[q(a)-q(b)]/2

              = [q(a)+q(b)]/2

SPHERE B=q(b)+[q(a)-q(b)]/2

                    =[q(a)+q(b)]/2