m$-$Xylene $($A$)$ transforms to p$-$xylene $($R$)$ and o$-$xylene $($S$)$ in two parallel liquid phase reactions. The transformation of m$-$xylene to p$-$xylene is a second order reaction with a rate constant of $0\mathrm{.}4$ m$3/$mol$.$min and the transformation of m$-$xylene to o$-$xylene is a first order reaction with a rate constant of $2$ min$-1.$ If the feed to a plug flow reactor contains $40$ mol$/$m$3$ m$-$xylene calculate the space time and the concentrations of p$-$xylene and o$-$xylene at the reactor exit for $90\%$ conversion of m$-$xylene.