If the original number can be written as ab, where a is the digits in the tens place and b is in the ones place, then it can be expanded as
10a + b
where a and b are chosen from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. The sum of the digits is 9, so
a + b = 9
Reversing the digits gives the number ba, or
10b + a
which is larger than ab by 45, so
10b + a = (10a + b) + 45
-9a + 9b = 45
a - b = -5
Solve for a and b :
(a + b) + (a - b) = 9 + (-5)
2a = 4
a = 2
Then
a + b = 9
2 + b = 9
b = 7
So the original number if (C) 27.