Question 7796
let the two digit number be xy
such that 10x  +y =xy
now as per question
x+y = 11   -----eq1

10y +x = 10x+y+9   ------eq2
or 9y-9x=9
multiply eq1 with9
so we have 
9x +9y = 99   ----eq3

add eq3 and eq2 we have

9x +9y = 99   
9y -9x = 9
---------------
18y = 108
y = 108/18 = 6
so x = 5   ( by substituting the value of y in eq1)

(Ans)