a
\(0.04=\mathrm{k}[\mathrm{A}]_0 \mathrm{e}^{-\mathrm{k} \times 10 \times 60}\)    \(...(1)\)

\(0.03=\mathrm{k}[\mathrm{A}]_0 \mathrm{e}^{-\mathrm{k} \times 20 \times 60}\)    \(...(2)\)

\((1) /(2)\)

\(\frac{4}{3}=\mathrm{e}^{600 \mathrm{k}(2-1)}\)

\(\frac{4}{3}=\mathrm{e}^{600 \mathrm{k}}\)

\(\ln \frac{4}{3}=600 \mathrm{k}\)

\(\ln \frac{4}{3}=600 \times \frac{\ln 2}{\mathrm{t}_{1 / 2}}\)

\(\mathrm{t}_{1 / 2}=600 \frac{\ln 2}{\ln \frac{4}{3}}\)sec

\(\mathrm{t}_{1 / 2}=600 \times \frac{\log 2}{\log 4-\log 3} \text { sec. }=10 \times \frac{0.3010}{0.6020-0.477} \mathrm{~min}\)

\(\mathrm{t}_{1 / 2}\)

Ans. \(24\)