Given, the sum of 2-digit number is 9

Let the unit digits of the number is x

then the tenth digit of the number is 9 - x

Now original number = 10(9-x) + x = 90 - 10x + x = 90 - 9x

Now digits of the numbers are interchanged.

So, unit digit = 9 - x

and tenth digit = x

The number = 10x + 9 - x = 9x + 9

According to the question,

      9x + 9 = 90 - 9x + 27

=> 9x + 9 = 117 - 9x 

=> 9x + 9x = 117 - 9

=> 18x = 108

=> x = 108/18

=> x = 6

So, the unit digit of the number = 6

and tenth digit of the number = 9 - x = 9 - 6 = 3

So, the required number = 36