The digits of a two-digit number add up to 11. When the digits are reversed, the new number is 27 more than the original. What is the original number?

Explanation

1. 01

   Let the number be $10a + b$ with $a + b = 11$.

2. 02

   Reversed minus original = $9(b - a) = 27$, so $b - a = 3$.

3. 03

   $a = 4$, $b = 7$: the number is 47. Check: $74 - 47 = 27$.