A two-digit number is 8 times the sum of its digits. When 45 is subtracted from the number, its digits get reversed. What is the number?

Explanation

1. 01

   Let the number be $10a + b$. Then $10a + b = 8(a + b)$, so $2a = 7b$.

2. 02

   Digits 0–9 force $a = 7$, $b = 2$ (or both zero, which is not a two-digit number).

3. 03

   Check the second condition: $72 - 45 = 27$, the reverse. So the number is 72.