A number has 2 digits whose sum is 9. If 27 is added to the number, its digits get interchanged. Find the number.

The correct answer is 36

Let the digit in the units place be x.
∴ The digit in the tens place will (9 - x)
∴ The number can be written as 10(9 - x) + x = 90 - 10x + x = 90 - 9x
The number with the digits interchanged = 10 x + (9 - x) = 10x + 9 - x = 9x + 9
∴ We can write the equation as follows
(90 - 9x) + 27 = 9x + 9
∴ 90 - 9x + 27 = 9x + 9
∴ 90 + 27 - 9 = 9x + 9x
∴ 108 = 18 x
∴ x = $\frac{108}{18}$ = 6
Thus the digit in the units place is 6 and the digit in the tens place is 9 - 6 = 3
Hence the number is 36