A number has two digits whose sum is 6. If 36 is added to the number, its digits get interchanged. Find the number.

The correct answer is 15

Let the digit in unit's place be x
∴ the digit in the ten's place will be (6-x)
The number can be calculated as 10(6-x) + 1(x)

After the digits are interchanged, the new number will be
10(x) + 1(6-x)

The equation can be written as follows
10(6-x) + 1(x) + 36 = 10(x) + 1(6-x)
60 - 10x + x + 36 = 10x + 6 -x
96 - 9x = 9x + 6
90 = 18x
or x = $\frac{90}{18}$ = 5
∴ The digit in unit's place is 5 and the digit is ten's place is (6 - 5) = 1
The number is 15