When the wire is bent to form a circle arc PQ subtends 90 degrees at the centre so the resistance of smaller part is 1/4 th of 10 ohms and bigger part is 3/4 of 10 ohms.
The resistance of the smaller arc is $2.5\Omega$ and that of the larger arc is $7.5\Omega$.
They are connected in parallel to each other and in series to the internal resistance.
total resiatance in the circuit is sum of the resiatances in parallel plus the internal resistance of the cell
Total resistance = (2.5) (7.5)/ 10 + 1 = 2.875
now total curreent in the circuit = 3/2.875 = 24/23
the current in the two branches of the circle will split according to the inverse of ratio of the resistance i.e. 1 : 3
i.e. 6/23 and 18/23
Ans : (D)