Auto$-$Moto receives about $800$ loan applications per month $(30$working days$).$ All applications go through an Initial Review sub$-$process, where the applications are then classified as A $($looks excellent$),$ B $($needs more detailed evaluation$),$ and C $($reject summarily$).$ A and B applications would be forwarded to sub$-$processes A and B$,$ respectively. On average, $16\%$ of all applications go through Sub$-$process A$,30\%$ go through sub$-$process B$,$ and the rest are rejected. On average, $50\%$ of applications in sub$-$process A$,$ and $15\%$ of applications in sub$-$process B are accepted and the rest are rejected. $($Recall that all Cs were rejected.$)$ On average $120$ applications are in the Initial Review sub$-$process, $30$ are in sub$-$process A$,$ and $10$ applications are in sub$-$process B$.$

$1.$ What is the average flow time of an application? The potential answers are:

A: $6\mathrm{.}4$ days.

B: $6\mathrm{.}12$ days.

C: $7\mathrm{.}5$ days.

D: $6$ days.

E: $9\mathrm{.}5$ days.