Answer
A long time after closing the switch $S$, the current through the central resistor will be equal to the current through the other resistor.
Work Step by Step
Just after the closing of switch $S$, current begins to flow through the circuit. This changing current through the inductor produces an emf in the opposite direction to the current flow. As time passes, the current through the inductor's branch of the circuit will increase exponentially to the equilibrium point where the current is equal in both branches of the circuit.
Therefore, a long time after closing the switch $S$, the current through the central resistor will be equal to the current through the other resistor.
