The completely mixed reactor is filled with $10$ L of an aqueous solution in which A is dissolved. The concentration of A in the reactor is $5$ x $10-3$ mol$/$cm$3.$

An aqueous solution containing A at a concentration of $1$ x $10-5$ mol$/$cm$3$ is supplied to the reactor at a rate of $2$ L$/$min$,$ and the aqueous solution is extracted from the reactor under stirring at a rate of $2$ L$/$min$.$

In this case, find the time $($min$)$ taken for the concentration of A in the reactor to become $10\%$ of the initial concentration in each of the following cases. There is no change in the density of the aqueous solution according to the change in concentration.

$1)$ If A is not responding

$2)$ A reacts at a rate of $-$rA$=0\mathrm{.}2$CA