On Mathland TV a political commentator summed up an election result as follows.

A Labour majority of 1729 last time has been turned into a Conservative majority of 1654 in this election and the conservative candidate has obtained 38% of the poll. Labour has taken second place. The Liberal Democrat has obtained only 14% of the poll and has been beaten into fourth place by the SNP candidate who has 50 more votes than the Liberal Democrat.

Given that there were just four candidates and that the figures quoted were exact find the number of votes polled for each candidate.
[This question comes from the book 'Mathematical Challenges' published in 1989 for the Scottish Mathematical Council by Blackie, ISBN 0216 92622X]