1. Problem: A two-digit positive integer has its digits reversed, and the resulting integer differs from the original by 27. Find the difference between the digits. 2. Let the tens digit be $x$ and the units digit be $y$. The original number is $10x + y$. 3. The reversed number is $10y + x$. 4. According to the problem, the difference between the original and reversed number is 27: $$| (10x + y) - (10y + x) | = 27$$ 5. Simplify the expression inside the absolute value: $$| 10x + y - 10y - x | = | 9x - 9y | = 27$$ 6. Factor out 9: $$9 | x - y | = 27$$ 7. Divide both sides by 9: $$| x - y | = 3$$ 8. Therefore, the digits differ by 3. Final answer: 3