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The discovery of gold in Victoria in mid 1851 led to the Victorian gold rush, and Melbourne, which served as the major port and provided most services for the region, experienced rapid growth. Within months, the city's population had increased by nearly three-quarters, from 25,000 to 40,000 inhabitants. Thereafter, growth was exponential and by 1865, Melbourne had overtaken Sydney as Australia's most populous city. Additionally, Melbourne along with the Victorian regional cities of Ballarat and Geelong became the wealthiest cities in the world during the Gold Rush era.

How much did Melbourne's population increase within months of the gold rush?
three-quarters, from 25,000 to 40,000 inhabitants