let the original number be 10x + y, where is x is the tens digit, y is the units digit

the sum of the digit of a two-digit number is 15

x + y = 15

the number formed by reversing the digits is less than the original number by 27

10y + x = 10x + y - 27

by solving the system of equations

x + y = 15

10y + x = 10x + y - 27

we find

x = 9

y = 6

click here to see the step by step solution of the system of equations

10*9 + 6 = 96

the original number is 96.