The sum of the digits of a two-digit number is 9. If 27 is added to the…

Let the two-digit number be 10x + y, where x is the tens digit and y is the units digit.

Given that the sum of the digits is 9, so x + y = 9.

Adding 27 reverses the digits, so the new number is 10y + x, and we have 10y + x = 10x + y + 27.

Rearrange that equation: 9y - 9x = 27, which simplifies to y - x = 3.

Now solve the system of equations:

x + y = 9

y - x = 3

Add the two equations: 2y = 12, so y = 6.

Then x = 9 - y = 3. Therefore the number is 10x + y = 36.

Verification: 3 + 6 = 9 and 36 + 27 = 63, which is the reversal of 36. So the answer 36 is correct.