The correct option is A Herself
Pronouns are words that replace nouns that have been mentioned before, to avoid repetition. There are many types of pronouns, one of them being the reflexive pronoun. A compound personal pronoun is formed by adding -self to personal pronouns my, your, him, her and -selves for plural pronouns your, our, them and so on. When an action done by the subject turns back (reflects) upon the subject, that compound personal pronoun is called a reflexive pronoun. In the given sentence, "The rich lady" is a subject as it performs an action "sat", she sat alone for some time, the term 'by+reflexive pronoun' means 'with no one else present'. Option A is correct, as the rich lady is of the feminine gender, 'her' is a personal pronoun suitable for her and 'herself' is the suitable reflexive pronoun that completes the phrase 'by herself'. Option B is incorrect, as 'himself' is used for the masculine gender, whereas the lady is mentioned here. Option C is incorrect as 'themselves' refers to a plural noun, whereas the 'lady' is a singular noun. Option D is incorrect, 'yourself' is from the second person point of view, it refers to the listener with whom the speaker is speaking, whereas 'lady' is in the third person point of view.