Private tuition is ordinary in Kolkata rather than exceptional, common enough that the question a family is answering is usually who, not whether. The school mix is worth weighing first — the state board sets its own Madhyamik and Higher Secondary papers, while many of the city's older convent and mission schools run ICSE, and the two reward quite different answer-writing.
A good deal of tuition in the city happens in batches at the tutor's own home, and for keeping pace with the class that works. It works less well when the problem belongs to one child in particular: a chapter missed during an illness, a subject that went wrong two years ago and was never repaired, a student who will not ask a question in front of eight others. That is usually the point at which a family starts looking for one-to-one time instead, and it is worth being clear which of the two you are hiring for.
Where the tutor lives still decides a great deal. Tutors on Tuitionites teach in Salt Lake, New Town, Ballygunge, Jadavpur, Garia, Behala, Dum Dum and Howrah, in person and online, and the newer eastern neighbourhoods are far enough from the older north and south of the city that an in-person slot has to be worth the journey for both sides. For a Higher Secondary student already carrying a coaching class, online is often what makes a second subject possible at all.