A gaseous fuel consists of $(30)$ vol$\%$ methane $($CH$4),(48)$ vol$\%$ hydrogen $($H$2)$ and $(22)$ vol$\%$ carbon monoxide $($CO$).$ The gross calorific values of methane, hydrogen, and carbon monoxide @$1$atm, $288$K are $37\mathrm{.}74$ MJ$/$m$3,12\mathrm{.}08$ MJ$/$m$3$ and $11\mathrm{.}97$ MJ$/$m$3,$ respectively. Calculate the net calorific value of the gaseous fuel $($MJ$/$m$3$ @ $1$atm, $288$K$)$ using the data given below. Data: $(1)$ Densities of methane, hydrogen, and carbon monoxide @$1$atm, $288$K are $0\mathrm{.}6787$ kg$/$m$3,0\mathrm{.}0853$ kg$/$m$3$ and $1\mathrm{.}1849$ kg$/$m$3,$ respectively. $(2)$ The molecular weights of C$,$ H and O atoms are to be taken as $12,1$ and $16,$ respectively. $(3)$ The latent heat of vaporization of water can be taken as $2\mathrm{.}447$ MJ$/$kg water.