The tens and units digits of a number are the same. When the number is added to its reverse, the sum is 110. What is the number?

Let the units digit be x. 
Then the tens digit is also x.
Therefore the number is 10x + x = 11x.On reversing the order of the digit the number is 10x + x = 11x.
Hence by the given condition we have,
11x + 11x = 110
        22x = 110
           x = 5
Therefore the required number is 55.