Preheat oven to 350 degrees.
Peel apples. Core, and cut into thin round slices.
Combine rum and sugar. Pour over apples. Let stand a hour.
Spread apricot preserves over bottom of an 8-inch round baking dish.
Arrange apple slices on top. Save juice.
Sprinkle apples with sugar.
Bake until soft and brown. Cool.
Heat liquid, pour over apples. Serve warm.