For the first order reaction, (A)$\to$products, the concentration of A changes from 0.1 M to 0.025 Min 40 min. The rate of reaction when the concentration of A is 0.01 M is 

For a first order reaction, we have 0.1 M of $\mathrm{A}\stackrel{t_{1/2}}{⟶}0.05\mathrm{M}$ of  $\mathrm{A}\stackrel{t_{1/2}}{⟶}0.025\mathrm{M}$ of A

Hence, $2t_{1/2}=40\min \text{ or }{t}_{1/2}=20\min .$ The rate constant of the reaction would be

$k=\frac{0.693}{t_{1/2}}=\frac{0.693}{20\min }=0.03465{\min }^{-1}$

The rate of rejection when [A]= 0.01 M would be 

$r=k\left[\mathrm{A}\right]=\left(0.03465{\min }^{-1}\right)\left(0.01\mathrm{mol} {\mathrm{dm}}^{-3}\right)=3.465\times {10}^{-4}\mathrm{mol} {\mathrm{dm}}^{-3}{\min }^{-1}$