If a sole executor or a sole universal or residuary legatee, or a person who would be solely entitled to the estate of the intestate according to the rule for the distribution of intestate's estates applicable in the case of the deceased, is a minor or lunatic, letters of administration, with or without the Will annexed, as the case may be, shall be granted to the person to whom the care of his estate has been committed by competent authority, or, if there is no such person, to such other person as the Court may think fit to appoint, for the use and benefit of the minor or lunatic until he attains majority or becomes of sound mind, as the case may be.