Does MTB tyres wear off fast in City - gravel pavement streets, city road? I want to buy a Cross country MTB that I want to use everyday to work within the city in weekdays. In weekends I want to take it for off-city roads with partially mud and grassy terrain. 

Will the MTB tyres wear off fast when using the city?
Yes, absolutely. The knobs will get rounded off at an accelerated rate, particularly down the center of the rear tire, and the tires won't offer as much traction off-road. This doesn't happen instantly, but it will happen soon enough on a knobby used for primarily road riding.