The rate of SN1 is decided by the stability of carbocation formed in the rate determining step.
Carbocation(D) is most stable due to +R effect of −OCH3 group; (C) is stabilised by +I and +H effects of the CH3 group; (B) is least stable due to − I effect of MeO group and (A) is stabilised by −CH3 as well as phenyl group. So increasing order of rate of SN1 is (B) <(A)<(C)<(D)