I've recently moved in to an apartment where the floor boards are damaged in some areas, presumably because there has been a lot of traffic in these spots. And it has been like this for years it seems, since the damage goes so deep. I'm attaching a photo.
I know I can't repair these much, I'm mostly looking to prevent further damage. My idea is to sand the area and carefully apply new white stain and new varnish. Never done this before though. How likely is it that the repairs will match the colour of the rest of the floor? Any advice on technique or products to use? Can I fill the "holes" with some kind of wood filler and then stain?