Brain-Teaser 120: Rugby results

From The Sunday Times, 14th July 1963 [link]

At a certain stage in our all-against-all Rugby football competition the table of results read as follows. There had been no matches in which neither side had scored at all:

What was the result of the match between A and B?

Note: This problem was set when a try was worth 3 points, a penalty goal 3 points and a converted try 5 points. Match points are on the usual basis of 2 for a win and 1 for a draw.

This puzzle was included in the book Sunday Times Brain Teasers (1974, edited by Ronald Postill).