A biomass gasifier operating with $180$ kg$/$h of biomass feeding rate is used to run a compression ignition engine. The engine has $32\%$ efficiency and operates in the duel fuel mode with $80\%$ diesel replacement. This gasifier$-$engine system produces $17,280$ MJ of energy per day. Calculate the gasifier efficiency if the calorific value of the biomass is $16$ MJ$/$kg$.$

$($a$)75\mathrm{.}0\%$

$($b$)70\mathrm{.}6\%$

$($c$)62\mathrm{.}5\%$

$($d$)54\mathrm{.}2\%$