§ 310. Personal service upon a partnership. (a) Personal service upon persons conducting a business as a partnership may be made by personally serving the summons upon any one of them. (b) Personal service upon said partnership may also be made within the state by delivering the summons to the managing or general agent of the partnership or the person in charge of the office of the partnership within the state at such office and by either mailing the summons to the partner thereof intended to be served by first class mail to his last known residence or to the place of business of the partnership. Proof of such service shall be filed within twenty days with the clerk of the court designated in the summons; service shall be complete ten days after such filing; proof of service shall identify the person to whom the summons was so delivered and state the date, time of day and place of service. (c) Where service under subdivisions (a) and (b) of this section cannot be made with due diligence, it may be made by affixing a copy of the summons to the door of the actual place of business of the partnership within the state and by either mailing the summons by first class mail to the partner intended to be so served to such person to his last known residence or to said person at the office of said partnership within the state. Proof of such service shall be filed within twenty days thereafter with the clerk of the court designated in the summons; service shall be complete ten days after filing. (d) Personal service on such partnership may also be made by delivering the summons to any other agent or employee of the partnership authorized by appointment to receive service; or to any other person designated by the partnership to receive process in writing, filed in the office of the clerk of the county wherein such partnership is located. (e) If service is impracticable under subdivisions (a), (b) and (c) of this section, it may be made in such manner as the court, upon motion without notice directs.