Statement-1: In neutral solution, there is partial precipitation of zinc sulphide by hydrogen sulphide gas. 

Statement-2: The complete precipitation of zinc sulphide takes place by hydrogen sulphide gas when alkali metal acetate is added to the solution.

$\mathrm{ZnS}$partial ppt. occurs in neutral solutions due to  $S^{\mathit{2}}-$ion conc. Derived from ${\mathrm{H}}_2\mathrm{S}$ is too severely reduced $\left[{\mathrm{H}}^{+}\right]$ Acid, preventing $K_{s}p$ of $\mathrm{ZnS}$from being significantly surpassed. By eliminating $\left[{\mathrm{H}}^{+}{\left]}_{\right(}\mathrm{Acid}\right)$ alkali solutions raise  $[S^{\mathit{2}}-)],$which increaseses the zinc sulphite precipitate. So,statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1.Hence, option B is correct.