What is the role of ${\mathrm{ZnCl}}_2$ in a dry cell?

During discharge of a lead storage battery, the density of ${\mathrm{H}}_2{\mathrm{SO}}_4$ fell from $1.294 \mathrm{g} {\mathrm{mL}}^{-1}$ to $1.139 \mathrm{g} {\mathrm{mL}}^{-1}$. Sulphuric acid of density $1.294 \mathrm{g} {\mathrm{mL}}^{-1}$ is $39\% {\mathrm{H}}_2{\mathrm{SO}}_4$ by weight and that of density $1.139 \mathrm{g} {\mathrm{mL}}^{-1}$ is $20\% {\mathrm{H}}_2{\mathrm{SO}}_4$ by weight. The battery holds $3.5$ litres of the acid and volume remains practically constant during discharge. Calculate ampere-hour of which the battery must have been used. The anode and cathode reactions during discharging are:

$\mathrm{Pb}+{\mathrm{SO}}_4^{2-}\to {\mathrm{PbSO}}_4+2{\mathrm{e}}^{-} \left(\mathrm{at} \mathrm{anode}\right)$
${\mathrm{PbO}}_2+4{\mathrm{H}}^{+}+{\mathrm{SO}}_4^{2-}+2{\mathrm{e}}^{-}\to {\mathrm{PbSO}}_4+2{\mathrm{H}}_2\mathrm{O} \left(\mathrm{at} \mathrm{cathode}\right)$

Which of the following reactions occurs at the cathode during charging of storage battery?