Chemical Kinetics: JEE Main 2025 Chemistry question

$\mathrm{A(g)\rightarrow B(g)+C(g)}$ is a first order reaction. Time: $t$, $\infty$; $p_{system}$: $p_t$, $p_\infty$. The reaction was started with reactant A only. Which of the following expression is correct for rate constant k ?