$N_1=N_0{e}^{-\lambda t_1}$

$\frac{N_1}{{ N}_0}=e^{-\lambda t_1}$

$0.67={\mathrm{e}}^{-\lambda t_1}$

$\ln \left(0.67\right)=-\lambda t_1$

${ N}_2=N_0{e}^{-\lambda t_2}$

$\frac{N_2}{{ N}_0}=e^{-\lambda t_2}$

$0.33={\mathrm{e}}^{-\lambda t_2}$

$\ln \left(0.33\right)=-\lambda t_2$

$\ln \left(0.67\right)-\ln \left(0.33\right)=\lambda t_1-\lambda t_2$

$\lambda \left(t_1-t_2\right)=\ln \left(\frac{0.67}{0.33}\right)$

$\lambda \left(t_1-t_2\right)\cong \ln 2$

$t_1-t_2\simeq \frac{\ln 2}{\lambda }=t_{1/2}$

Half life $=t_{1/2}=20$ minutes.