At 30   ° C , the half life for the decomposition of AB 2 is 200   s and is independent of…

Since half life is independent of intial concentration of the reactant, it's a first order reaction

$\mathrm{k}=\frac{\ln 2}{{\mathrm{t}}_{\frac{1}{2}}}$
$\mathrm{kt}=2.303 \log \frac{{\mathrm{A}}_0}{\mathrm{A}}$

$\frac{\ln 2}{{\mathrm{t}}_{\frac{1}{2}}}\mathrm{t}=2.303 \log \frac{{\mathrm{A}}_0}{\mathrm{A}}$

$\frac{2.303 \log 2}{200}\mathrm{t}=2.303 \log \frac{100}{20}$

$\mathrm{t}=\frac{200}{0.3}\times \log 5=466.67 \sec \approx 467 \sec$