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?

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