GATE Civil Engineering (CE) 2018 Shift 2 Solved Paper

A schematic flow diagram of a completely mixed biological reactor with provision for recycling of solids is shown in the figure.${\mathit{S}}_0,\mathit{S}=$ readily biodegradable soluble $\mathit{B}\mathit{O}\mathit{D},\mathit{m}\mathit{g}/\mathit{L}$
$\mathit{Q},{\mathit{Q}}_{\mathit{r}},{\mathit{Q}}_{\mathit{w}}=$ flow rates,
${\mathit{X}}_{0\mathit{\ell }}{\mathit{X}}_{\mathit{k}}{\mathit{X}}_2,{\mathit{X}}_{\mathit{u}}=$ microorganism concentrations (mixed-liquor volatile suspended solids or MLVSS), $\mathit{m}\mathit{g}/\mathit{L}$
The mean cell residence time (in days, up to one decimal place) is ___________