An uncharged spherical conducting shell surrounds a charge –q at the center of the shell. Then charge +3q is placed on the outside of the shell.
When static equilibrium is reached, the charges on the inner and outer surfaces of the shell are respectively:

a) +q, -q
b) -q, +q
c) +q, +2q
d) +2q, +q

a) The the charges on the inner and outer surfaces of the shell are respectively +q, -q

Explanation:

Under static equilibrium inside a conductor, the total electric field, E = 0

This must be zero so that no charge will be moving since the conductor is in static equilibrium.

Also, since Electric field, E is zero, then flux through the surface will zero.

From Gauss' law, the total charge enclosed is zero.

Given –q as the  charge at the center of the shell, then the opposite charge on inner surfaces  will be +q, so that the total charge enclosed will be zero.

Since the charge is in static equilibrium, then opposite charge will be on the surface, that is –q.

Therefore, the the charges on the inner and outer surfaces of the shell are respectively +q, -q