$CH _{3}- \overset{+}{C}H - OCH _{3}$ is most stable due to resonance
Carbocation $CH _{3}-\overset{+}{ C}H - COCH _{3}$ is least stable due to electron withdrawing nature of carbonyl group. Carbocation $CH _{3}- \overset{+}{C}H - CH _{3}$ is less stable than
$CH _{3}- \overset{+}{C}H - OCH _{3}$ because it stabilised only by the $+I$ effect of the two methyl groups.
Therefore, correct order of decreasing stability is $II > I > III$
