Statement-1: Initially there is no ppt. when ${\text{ AgNO}}_3$ is added to ${\mathrm{Na}}_2{\mathrm{SO}}_3$ solution.

Statement-2: Localized formation of ${\mathrm{Ag}}_2{\mathrm{SO}}_3$ is destroyed by soluble complex formation like ${\left[{\mathrm{AgSO}}_3\right]}^{-}$.

When ${\text{ AgNO}}_3$ is introduced to ${\mathrm{Na}}_2{\mathrm{SO}}_3$ solution, there is initially no ppt because localized ${\text{ AgNO}}_3$ formation is shattered by the creation of soluble complexes such $\left[{\mathrm{AgNO}}_3\right]$.

Hence, option A is correct.