A gasoline fuel comprising $30$ mass $\%C_7{H}_{16}$ and $70$ mass $\%C_8{H}_{18}$ is fed to a combustion chamber with an excess of $100\%$ air over that required for complete combustion. The fractional conversion of both fuels is $85\%$ and the resulting combustion gases contain $10$ times as much $C{O}_2$ as $CO,$ along with water vapour, excess oxygen, nitrogen and unburnt fuel. Assuming that air is $21$mol$\%O_2$ and $79$mol$\%N_2,$ calculate

$($c$)$ the mole fractions of the combustion gases

Notes and hints: RMM C $=12,H=1,O=16,N=14$ and try using an atomic balance to calculate the mole fractions of the combustion gases and start with $100kg$ of fuel as your basis.