Answer :

Let the two digit number be = 10 x + y
Given: Sum of digits of two digit number = 9, x + y = 9
So, if one of the digit is x, second digit will be 9 - x
So we have our 2 digit number = 10 x + (9 - x)
Reversing the digits of this number = 10 (9 - x) + x
Now it is given that 
resulting new number is greater than the original number by 27.
Therefore, 10(9 - x) + x - (10 x + 9 - x) = 27
90 - 10 x + x - 10 x - 9 + x = 27
81 - 18 x = 27
18 x = 81 - 27
18 x = 54
x = 54/18
x = 3
So the number is 10 x 3 + (9 - 3) = 36
 

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