On reversing the digits of a two digit number, the number obtained is 9 less than three times the original number. If the difference of these two numbers is 45, find the original number. 

Let the ones place digit be y and the tens place digit be x.

The original number = 10x + y

The reversed number = 10y + x

Step 1: Formulating the Equations

1. Condition 1: According to the question,

   3(10x + y) - 9 = 10y + x

   Simplify:

   30x + 3y - 9 - 10y - x = 0

   29x - 7y - 9 = 0

   (1) 29x - 7y - 9 = 0

2. Condition 2: As the reversed number is bigger,

   10y + x - (10x + y) = 45

   Simplify:

   10y - 10x + x - y - 45 = 0

   9y - 9x - 45 = 0

   y - x - 5 = 0

   (2) y = x + 5

Step 2: Solving the Equations

Substitute Equation (2) into Equation (1):

29x - 7(x + 5) - 9 = 0

Simplify:

29x - 7x - 35 - 9 = 0

22x = 44

x = 2

Step 3: Finding y

Substitute x = 2 into Equation (2):

y = x + 5

y = 2 + 5 = 7

Final Answer

The original number is 27, and the reversed number is 72.