The sum of the digits of a two digit number is 13 the number obtained by interchanging its digits exceeds the given number by 9 find the original number

Let the unit digit be 'x' and tens digit be 'y'
So, x + y = 13 ...............(1)
The original number is 10y +x
if the digits are interchanged, the number becomes 10x+y
Now, 10x+y = 10y+x +9
or, 10x+y-10y-x = 9
or, 9x -9y =9
or, 9(x-y) =9
or, x - y = 1 ........................(2)
Adding equtions (1) and (2) gives
2x = 14
or, x =7
So, y = 13-x = 13-7 =6
Hence, the original number = 67 Ans.