The rate of first-order reaction is $0.04 \mathrm{mol}$ ${\mathrm{L}}^{-1}$${\mathrm{S}}^{-1}$ at 10 seconds and $0.03 \mathrm{mol}$${\mathrm{L}}^{-1}$${\mathrm{S}}^{-1}$  at 20 seconds after initiation of the reaction. The half-life period of the reaction is

 For a first order reaction, $A\to$ Products  and  for concentration of the reactant at two different times,

$\mathrm{k}=\frac{2.303}{{\mathrm{t}}_2-{\mathrm{t}}_1}\log \frac{[\mathrm{A}{]}_1}{[\mathrm{A}{]}_2}$

$\therefore \mathrm{k}=\frac{2.303}{{\mathrm{t}}_2-{\mathrm{t}}_1}\log \frac{(\text{ rate }{)}_1}{(\text{ rate }{)}_2} (\because \text{ rate }\propto [\mathrm{A}\left]\right)$

$\mathrm{k}=\frac{2.303}{(20-10)}\log \left(\frac{0.04}{0.03}\right)=0.0287{\sec }^{-1}$

${\mathrm{t}}_{1/2}=\frac{0.693}{\mathrm{k}}=\frac{0.693}{0.0287{\sec }^{-1}}=24.14\sec$