Mirzapur, a city in Uttar Pradesh, declined in importance when the railway link to Bombay started operating. Mirzapur was a crucial port for trade, notably for goods like cotton, silk, and carpets, due to its location along the Ganges. When the railway link was established, direct trading routes opened up that were faster and more efficient than the riverine route. Due to this, the prominence of Mirzapur as a trade hub declined.

Option 1, Benaras, remained significant due to its religious importance, and options 2 and 4, Kanpur and Patna, were vital for their industrial and administrative capacities, respectively. While these cities also relied on the Ganges for trade, their importance did not decline significantly with the advent of railway links.

So, the correct response to the question: "Which one of the following cities on the banks of the Ganges declined in importance when the railway link to Bombay started operating?" is option 3, Mirzapur.