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

The 2 digit number is 36.

Step-by-step explanation:

Let the 2 digits be x and y. The 2 digit number is xy.

x + y = 9 ... (1)

The old number can be written as 10x + y and the new number as 10y + x.

10y + x = 10x + y + 27

9x - 9y = - 27

x - y = - 3 ... (2)

Adding (1) and (2) we get:

2x = 6

x = 3

and therefore y = 9-3 = 6.