Strain liquid from can of beets into small saucepan. Set beets aside.
Combine both vinegars, sugar and salt with beet liquid in saucepan.
Bring to a boil and simmer for 5 minutes.
Put eggs in an appropriate sized jar. Put beets on top.
Pour vinegar mixture over eggs and beets in jar.
Cover and refrigerate. Try to forget about them for a few days - at least two days. Three days and they're awesome...a few days more and they're perfect.