Reversing the digits of a two-digit number

A two-digit number has tens digit \(a\) and ones digit \(b\).

1. The sum of the digits is \(11\), and reversing the digits gives a number \(27\) greater. Form two equations and find the number.[3]
2. Show that, for every two-digit number, the reversed number minus the original number is a multiple of \(9\).[2]
3. Explain why no two-digit number increases by exactly \(30\) when its digits are reversed.[1]
4. How many two-digit numbers increase by exactly \(27\) when their digits are reversed?[1]