The average of the two-digit numbers, which remain the same when the dibits inter-change their positions, is :

Average = (11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99) / 9

             =( (11 + 99) + (22 + 88) + (33 + 77) + (44 + 66) + 55) / 9

             = (4 * 110 + 55)/9 =  495 / 9 = 55.