How much does time does the ArcGIS solar radiation tool take to give solar map for day of about 50 km area?
That depends on you data resolution and computer specifications including RAM and processing power. It took me about 1-day to do a college campus at about 2m resolution.
I cannot link to GeoNet as it is behind a log in wall but on this forum I found that,
"We are using the tool to calculate direct and diffuse incoming solar radiation for a valley in the mountains. The cell size of the raster is 1 m x 1 m and it has around 45'000 columns by 42'000 rows - it's quite big. We try to calculate the radiation for the period of a whole year with a time interval of 14 days and 0.5 hours. The output will be a single file."
This took about 1 month on a high spec PC.