Teaser 2742: Hymns bored

From The Sunday Times, 12th April 2015 [link] [link]

Peter became bored during the Sunday service, so his mind turned to the three three-figure hymn numbers displayed on the board, all chosen from the five hundred hymns in the hymnal. He noticed that the sum of the digits for each hymn was the same, that one hymn number was the average of the other two, and that no digit appeared more than once on the board.

What (in increasing order) were the three hymn numbers?

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