A two-digit number becomes 45 less when its digits are reversed. If the sum of the digits in the reversed number is 13, what is the original number?

Explanation

Let the original number be 10a + b, where a and b are its digits. When digits are reversed, the number becomes 10b + a. Given that the reversed number is 45 less than the original: (10a + b) - (10b + a) = 45, which simplifies to 9a - 9b = 45 or a - b = 5. Also, the sum of digits in the reversed number is a + b = 13. Solving these two equations: a - b = 5 and a + b = 13, we get a = 9 and b = 4. Therefore, the original number is 94.