Final answer:
The main purpose of the described encounter with the British family is to emphasize the protagonist's response to societal perceptions and assumptions.
Step-by-step explanation:
The main purpose of the described encounter with the British family in the passage from A Visit to Europe by T. N. Mukharji is to emphasize the protagonist's response to societal perceptions and assumptions. The protagonist, Mukharji, uses the family's curiosity and stereotypes as an opportunity to engage with them playfully and challenge their assumptions about him. Through his interaction with the family, Mukharji breaks down societal barriers and showcases his ability to speak English, which surprises and impresses the family.