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