Define original value of the two digit
I make an example, a is the first digit and b is the second digit. The original value of the digit will be
10a + b
because a stands as tens and b stands as units
Make an equation system
The sum of two digit is 15
⇒ a + b = 15 (this is first equation)
If the digits are reversed, the new number is 27 less than the original number. That means b will stand as tens, and a will stand as units.
⇒ 10b + a = (10a + b) - 27 (this is second equation)
Solve the equation
To find the numbers, we should solve the first and second equation.
From the first equation
a + b = 15
a = 15 - b
Subtitute 15 - b to a in the second equation
10b + a = 10a + b - 27
10b + (15 -b) = 10(15 - b) + b - 27
9b + 15 = 150 - 10b + b - 27
9b + 10b - b = 150 - 27 - 15
18b = 108
b = 6
Subtitute 6 as b to the first equation
a = 15 - b
a = 15 - 6
a = 9
The original number is 96