C$5$H$10$ fuel is burned with $20$ percent excess air. If the upper calorific value of this fuel is $42\mathrm{.}45$ MJ$/$kg and the enthalpy of vaporization of water at $25\backslash$deg C is $2442\mathrm{.}3$ kJ$/$kg$,$ calculate the following parameters.

$($a$)$ air fuel ratio

$($b$)$ Equivalence ratio

$($c$)$ Lower calorific value of the fuel $($MJ$/$kg$)$