Answer
Just after switch $S$ is reopened, the current through the central resistor will be equal to the current through the other resistor.
Work Step by Step
After switch $S$ is reopened, the battery is eliminated from the circuit, so the current starts to decrease. This changing current through the inductor produces an emf across the inductor so the current decreases exponentially to the equilibrium point when the current is zero.
Because switch $S$ is open, the current flow through both resistors is equal since the circuit has a single loop consisting of the inductor and both resistors.
Therefore, just after switch $S$ is reopened, the current through the central resistor will be equal to the current through the other resistor.
