$$\begin{aligned} & L=\mu_0 \mu_r \times n \times A \times N \\ & L=\mu_0 \mu_r n \times A \times \frac{N}{I} \times I \\ & L=\mu_0 \mu_r \times n^2 \times A \times I \Rightarrow L \propto n^2 I \\ & \Rightarrow \frac{L_A}{L_B}=\frac{n_A^2}{n_B^2} \times \frac{I_A}{I_B} \\ & \Rightarrow \frac{L_A}{L_B}=\frac{1}{4} \times 2=\frac{1}{2} \end{aligned}$$