Half-life periods for a reaction at initial concentration of $0.1\mathrm{M}$ and $0.01\mathrm{M}$ are 5 and 50 minutes respectively. Then the order of reaction is

When the initial concentration is reduced from$0.1\mathrm{M}$ to $0.01\mathrm{M}$, the half-life period of the reaction increases from 5 minutes to 50 minutes.
Thus, when the initial concentration is reduced to one-tenth, the half-life period becomes 10 times.
Hence, the half-life period is inversely proportional to the initial concentration
$\left({\mathrm{t}}_{1/2}\propto \frac{1}{ \mathrm{A}}\right)$
This is true for the second-order reaction.