The time period of the second's pendulum = $2 \mathrm{s}$

Change in the time period, $\Delta \text{T}=\frac{1}{2}\text{T}\alpha \Delta \theta$

$\Delta \text{T}=\left(\frac{1}{2}\right) \left(2\right) \left(1\text{.}2\times 10^{-5}\right) \left(30^{\circ }-20^{\circ }\right)$

       $=1\text{.}2\times 10^{-4}\text{ s}$

New time period, ${\text{T}}^{\prime }=\text{T}+\Delta \text{T}$

                             ${\text{T}}^{\prime }=2\text{.}00012\text{ s}$

Time lost in a week,

                   $\Delta \text{t}=\frac{\Delta \text{T}}{{\text{T}}^{\prime }}\times \text{t}$

                        $=\frac{1\text{.}2\times 10^{-4}}{2\text{.}00012}\times \left(7\times 24\times 3600\right)$

                        $=36\text{.}28\text{ s}$