Removing floor plans back ground

Okay, it's not going to be simple, which I'm sure you know already. I don't think you are going to be able to get the colored rooms completely transparent without a lot of work. The small type is not going to look good when you try to remove the background colors quickly. There are a few techniques you can experiment with. Do a general search for tutorial videos on how to remove the background from drawings in Photoshop and you'll get some ideas.

You'd still need to isolate each room background color in order to use the Select > Color Range tool to get a sample. Be sure to convert layers to smart objects for non-destructive editing. Unless this is a mission-critical project, I think you should take the easy route and remove the majority white, then add a Gradient layer to your liking. Or, recreate the floor plan in another program without the colors. Others may have more advice for you and best of luck with the project.