The sum of a two digit number and the number formed by interchanging the digit is 12 is added to the number, the new number becomes 5 times the sum of the digits. Find the number.

Explanation

To solve the problem step by step, we will define the two-digit number and set up equations based on the information provided in the question.

### Step 1: Define the Variables
Let:
- \( x \) = unit digit of the two-digit number
- \( y \) = ten's digit of the two-digit number

Thus, the two-digit number can be expressed as:
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