Hi, In my office we have several door sets which are a leaf & half. The half leaf has no bolts so can just be pushed open. If both doors get pushed open together the half leaf will not close and hits on the main door. Is this an installation problem. Should the half leaf close even if opened first.?

Your doorsets no doubt are missing these: https://wellinguk.com/products/door-closers/door-closers-door-closers/overhead-surface-mounted-door-closers/double-door-selector-silver/

Are the doors rebated at their meeting edges?  If so, a door selector is required. If not, a repair is required. 

Thank you for the replies. The leaves have square edges and both have closers but half leaf overlaps the main door when closed so prevents from closing into frame.

A suitable repair by a competent person is required.

Might it have been a simple mistake on original installation? It is common to provide a door and a bit to some offices to allow bulky furniture and other items to be moved in and out. The smaller leaf is retained with shoot bolts without a door closer.