Given that,

- $3p-q<4 \quad \longrightarrow (1)$
- $3q-p<12 \quad \longrightarrow (2)$

Adding the equation $(1)\; \& \; (2).$

$3p-q + 3q-p < 4 + 12$

$\Rightarrow 2p + 2q < 16$

$\Rightarrow 2(p + q) < 16$

$\Rightarrow {\color{Green} {\boxed{p + q < 8}}}$

Correct Answer $:\text{A}$