In medium saucepan, cover beets with water and bring to a boil. Reduce to a simmer and cook 35 to 40 min. until beets are tender. Remove beets and cool completely; reserve 2 cups (500 mL) cooking liquid.
Stir together reserved cooking liquid, vinegar, sugar and salt -- until sugar is dissolved; set aside to cool completely.
Peel and quarter beets. Place beets and eggs in mason jar. Pour pickling liquid into jar (be sure it completely covers beets and eggs). Seal jar and refrigerate at least 24 hr. before eating. (Note: The longer the beets and eggs stay in the pickling liquid, the more intense their flavour.) Store refrigerated up to 2 weeks.
Flavour pickling liquid with 2 tbsp (30 mL) pickling spices or add fresh or dried spicy chili peppers.
For even quicker pickle, use jarred beets and the juice from canned beets to make the pickling liquid.