About the universal morphism from the pushout of monomorphisms.

Question

Let $A,B,C$ be objects in a category $\mathrm{C}$ and we have the pushout diagram of monomorphisms$\require{AMScd}$ \begin{CD} C @>>> A\\ @VVV @VVV\\ B @>>> A\bigsqcup\limits_C B\end{CD} Now consider another object $X$ in $\mathrm{C}$ such that the below diagram is a pullback square of monomorphisms. \begin{CD} C @>>> A\\ @VVV @VVV\\ B @>>> X\end{CD}That is $C=A\times_XB$. What conditions are necessary on the category $\mathrm{C}$ so that the universal morphism from the pushout $A\bigsqcup\limits_CB\to X$ is a monomorphism?