Question 970588
Let 10x + y be the two digit number.
The reverse number is 10y + x.
Given that the sum of two digit number and its reverse is 99.
=> (10x + y) + (10y + x) = 99
=> 11x + 11y = 99
=> x + y = 9
The two digit numbers that can satisfy this condition are 
45,54
27,72
81,18
36,63
90