For a first order reaction ${A(g) \to 2B(g) + C(g)}$ at constant volume and $300\, K$, the total pressure at the beginning $(t = 0)$ and at time $t$ are $P_0$ and $P_t$, respectively. Initially, only $A$ is present with concentration $[A]0$, and $t_{1/3}$ is the time required for the partial pressure of $A$ to reach $1/3^{rd}$ of its initial value. The correct option(s) is (are)
(Assume that all these gases behave as ideal gases)