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A large number of Indians came to East Africa from Gujarat in the 19th and early 20th centuries. A smaller number came to modern Tanzania than to Uganda or Kenya.
The reason for the larger number to the other two countries was the importation of laborers for the building of the Kenyan Ugandan railroad. The ones who went to Tanzania were mostly traders, which is to say that they travelled in relative comfort ("business class" if not first class) on the ships of the time.