Question

The sum of the digits of a certain two-digit number is 11. When you reverse its digits you increase by 9. What is the number?

Answer 1

the number is composed by two digits, let them be ab, so we have:
a + b = 11

this is a pseudo-equation, we are not multiplying ab or ba, is just the digits order.
ba = ab + 9
The pairs of numbers that could comply with the first equation are:
(2,9)
(3,8)
(4,7)
(5,6)
But only the last couple (5,6) comply as well with the second condition. Because 65 = 56 + 9
Therefore the unknown number is 56