Activity of $S_1=\frac{1}{2}$ (activity of $S_2$ )
or

\lambda_2 N_1=\frac{1}{2}\left(\lambda_2 N_2\right) \text { or } \frac{\lambda_1}{\lambda_2}=\frac{N_2}{2 N_1}

or

$$\begin{aligned} & \frac{T_1}{T_2}=\frac{2 N_1}{N_2}\left(T=\text { half-life }=\frac{\ln 2}{\lambda}\right) \\ & N_1=2 N_2 \\ & \frac{T_1}{T_2}=4 \end{aligned}$$

Given
$\therefore$ correct option is (a).