Sum of the digits of a two digit number is 9. When we interchange the digit it is found that the resulting new number is greater than the original number by 27. What is the two digit number?

Let the digits at tens place and ones place: x and 9−x respectively.
∴original number=10x+(9−x)=9x+9
Now Interchange the digits: Digit at ones place and tens place: x and 9−x respectively.
∴New number: 10(9−x)+x=90−10x+x=90−9x
AS per the question
New number=Original number+27
90−9x=9x+9+27
90−9x=9x+36
18x=54
x=54/18
x=3
Digit at tens place →3 and one's place :6
∴Two digit number:36