Sum of the digits of a 2 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 2 digit number?

The 2 digit number is 36

Step-by-step explanation:

Let the 2 digits be x and y, then:

x + y = 9

10y + x = 27 + 10x + y

From the second equation:

-9x + 9y = 27 Divide through by 9:

-x + y = 3 Add this to th first equation:

2y = 12

y = 6.

and x = 9 - 6 = 3.