Orange juice is aseptically packed in a laminated pouch and held at $25C.$ The degree of browning as optical density $($OD$)$ at $420nm$ measured on first day is $0\mathrm{.}10$ in juice. The browning reaction follows a zero$-$order reaction. The rate constant for juice is $2\mathrm{.}375{10}^{-3}OD$ day. Calculate the shelf life of juice in days if the juice becomes unacceptable when degree of browning exceeds $0\mathrm{.}30OD.$

$($a$)74$

$($b$)104$

$($c$)94\mathrm{.}6$

$($d$)84\mathrm{.}2$