Observe the following reactions at $T(K)$:
$I. A \rightarrow \text{products}$
$II. 5Br^{-}_{(aq)} + Br{O_{3}}^{-}_{(aq)} + 6H^{+}_{(aq)} \rightarrow 3Br_{2(aq)} + 3H_{2}O_{(l)}$
Both the reactions are started at $10.00 \text{ am}$. The rates of these reactions at $10.10 \text{ am}$ are same. The value of $-\frac{\Delta[Br^{-}]}{\Delta t}$ at $10.10 \text{ am}$ is $2 \times 10^{-4} \text{ mol L}^{-1} \text{ min}^{-1}$. The concentration of $A$ at $10.10 \text{ am}$ is $10^{-1} \text{ mol L}^{-1}$. What is the first order rate constant (in $\text{min}^{-1}$) of reaction $I$?

• A
  $2 \times 10^{-3}$
• B
  $10^{-3}$
• C
  $10^{-2}$
• D
  $4 \times 10^{-3}$