Question 259429
Let the number be xy.
Given,the sum of the digits of a two digit number is 15.
                            x+y = 15  ...(1)
Also, if the digits are interchanged the result exceeds the original number by 9. 
               10y+x=10x+y+9
               10y+x-10x-y=9
               9y-9x=9
               y-x=1     ...(2)
(1)+(2) =>     2y = 16
               y = 16/2 = 8
(1) =>         x+8=15
               x=15-8=7
Therefore the given number is 78