Let the two digits of the number be 10s digit x and 1s digit y
The number is 10x + y
The sum of two digits of a number is 15.
x + y = 15
x = 15-y Eq..1
If 9 added to the number, then are reversed
10x + y + 9 = 10y + x
10x - x + y - 10y = -9
9x - 9y = -9
x - y = -1
Substituting the value of x from Eq..1 to Eq..2
x - y = -1
15 - y - y = -1
-2y = -1 - 15
2y = 16
y = 16/2
y = 8
Thus 1s digit is 8
Substituting value of y in Eq…1 to derive value of x.
x = 15 - y
x = 15 - 8
x = 7
Thus 10s digit is 7
The number is 78