(b) That's right. A contractual duty to exercise reasonable care and skill is implied by law into contracts for professional services, for example, by lawyers; accountants; bankers; consultants and advisers; and medical practitioners. But the law does not go so far as to require the providers of professional services to act in the best interests of their client.
In the example, B is therefore not in breach of an implied contractual term to act in A's best interests.