These are neighboring group participation reactions. You can draw five-membered intermediates for
B and
C. Since these are solvolysis reactions, it is difficult to predict what the products are. According to
Reusch, "Since the SN1 and E1 reactions proceed via the same carbocation intermediate, the product ratios are difficult to control and both substitution and elimination usually take place." Elimination can give different products.
B and
C can give discreet products due to the neighboring group, though with a net epimerization for
B.