Strain liquid from beets into small saucepan. Set beets aside. Combine both vinegars, sugar & salt with beet liquid in saucepan. Bring to boil & simmer for 5 minutes. Put eggs in an appropriate sized jar. Put beets on top. Pour vinegar mixture over eggs & beets in jar. Cover & refrigerate. Try to forget about them for 3 or more days (I prefer 5-7).