In these questions, you are typically being judged on your structured thinking and business sense. What actually matters is how you approach, rather than the actual answer.
You can look at this guide - this is an awesome resource for preparing for analytics interviews with links to guess-estimates and case studies:
If I was asked this question in an interview, here is one possible answer:
I would divide entire Bangalore in a suitable grid, say based on PinCode or area, then look at customer characteristics for each of the area. Here are a few things I will look at:
- Population of the area
- Targetable customer base for each product the bank can offer
- Average income for each of these areas
- Competition index illustrating how much competition is already there (Higher index = low competition, 1 in case when there is no other bank).
Next you can create a metric like (targetable customer base x acquisition factor x average profitability from customer in a 3 year period x competition factor). The area with highest value looks like the best area to open a bank.
There can be other factors like security concerns (theft record in the area), existing customers / referral channel partners (if any), which can also play a role in this decision.
Hope this gives you a direction.