A radioactive sample $S_1$ having an activity of $5\mu Ci$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10\mu Ci$. The half lives of $S_1$ and $S_2$ can be

Given:   $R_1=5\mu ci,R_2=10\mu ci,N_1=2N_2$ 

By,   $\lambda N=R$ 

        $\frac{0.693}{T}N=R$ 

        $T=\frac{0.693N}{R}$ 

For sample $S_1$:

             $T_1=\frac{0.693N_1}{5}$ 

             $T_1=\frac{0.693\times 2N_2}{5}$ ......................eq1,

For sample $S_2$: 

             $T_2=\frac{0.693N_2}{10}$ ....................eq2,

By dividing eq1 by eq2, we get:

             $\frac{T_1}{T_2}=\frac{4}{1}$ 

It is clear that the ratio of half lives of the two samples is $4:1$, therefore half lives can be $20$ ($4k$) years and $5$ ($1k$) years respectively.