Let the number be x and y.
Given, x+ y= 11 --------------------(1)
and 10x + y = 10y +x +45
or 9x - 9y = 45
or x -y =5 ----------------(2)
On adding eq (1) and (2) we get:
2x = 16 or x = 8
putting the value of x in eq(1) we get:
8 + y = 11
or y = 3
Therefore, the original number is 83.