Answer
75.9 min is needed to decay 92.5%.
135 min is needed to decay 99.0%.
Work Step by Step
Amount of radionuclide at the beginning $A_{0}=100$
When 92.5% is decayed,
Amount of radionuclide remaining
$A= 100.00-92.5=7.5$
Rate constant $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{20.3\,min}=0.034138\,min^{-1}$
$\ln(\frac{A_{0}}{A})=kt$
$\implies \ln(\frac{100}{7.5})=2.59=0.034138\,min^{-1} \times t$
Or $t= \frac{2.59}{0.034138\,min^{-1} }=75.9 \,min$
When 99.0% is decayed,
Amount of radionuclide remaining
$A=100-99=1$
Then,
$ \ln(\frac{100}{1})=4.605=0.034138\,min^{-1} \times t$
$\implies t= \frac{4.605}{0.034138\,min^{-1}}=135\,min$
