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Mathland Election

Age 11 to 14 Challenge Level:

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]