I have a multiple-entry tourist visa -C for Schengen countries for a validity of 6 months. I applied for a business visa but the files sent back from the Embassy state that a valid visa is already on passport.
How would I handle an entry immigration check? They will ask the purpose of my visit and I would say business, yet the visa is a tourist one.
No, your visa is a uniform short-stay visa.
The Schengen system does not have different kinds of visas for business and tourism. Your visa is valid for all short visits to the Schengen area.
In the application form there is a question that asks for "purpose of stay" -- but that does not mean "which kind of visa should we issue?", rather "which general kind of story are you going to tell with your documentation to convince us that we should issue you a visa?".
In particular, since you were issued a visa with multiple entries, there is no expectation whatsoever that your subsequent visits will be the same visit (with the same purpose) as the one you described in your original application.
