Solution :
Comparing the solubility of silver chromate for the solutions :
[tex]$0.10 \ M \ AgCH_3COO$[/tex] ----- Less soluble than in pure water.
[tex]$0.10 \ M \ Na_2CrO_4$[/tex] ----- Less soluble than in pure water.
[tex]$0.10 \ M \ NH_4NO_3$[/tex] ----- Similar solubility as in the pure water
[tex]$0.10 \ M \ KCH_3COO$[/tex] ----- Similar solubility as in the pure water
The silver chromate dissociates to form :
[tex]$AgCrO_4 (s) \rightleftharpoons 2Ag^+ (aq) +CrO_4^{2-}(aq)$[/tex]
When 0.1 M of [tex]$AgCH_3COO^-$[/tex] is added, the equilibrium shifts towards the reverse direction due to the common ion effect of [tex]Ag^+[/tex], so the solubility of [tex]Ag_2CrO_4[/tex] decreases.
Both [tex]AgCH_3COO[/tex] and [tex]$KCH_3COO$[/tex] are neutral mediums, so they do not affect the solubility.