"How do you do?" is formal and mostly only used in quite "upper class" circles these days. The formal, proper way to reply is indeed to say the same. It's not a

"How do you do?" is formal and mostly only used in quite "upper class" circles these days. The formal, proper way to reply is indeed to say the same. It's not an actual question, think of it as a more of a greeting. Some members of the Royal family were reported to refer to the Middletons (Prince William's in-laws) as the "great to meet you" in a condescending way because they were said to be saying that instead of "how do you do?" when introduced to people/them... Language has always been a social class differentiator.