(a) Force is repulsive means both the spheres have same charge.
The total charge on the two non-conducting sphere is.
Q1 + Q2 = 9*10^-5 C
The force between the two spheres is,
F = k * (Q1 * Q2) / r^2
Q1Q2 = 1.5x10^-9
Q1(9*10^-5-Q1) = 1.5x10^-9
On solving this quadratic we get,
Smaller charge as 2.21x10^-5 C
Larger charge as 6.79x10^-5 C
(b) Smaller charge is -1.44x10^-5 C
Larger charge is 1.04x10^-4 C