The sum of the digits of a two digit number is 9. On adding 27 to the number , its digits are reversed. The number is

1. 36
2. 45
3. 54
4. 72

Let the digit in the units place be x.

Since the sum of the digits is 9, the digit in the tens place must be (9 - x).

A two-digit number is written as: 10 x (Tens digit) + (Units digit)

Original Number = 10(9 - x) + x

= 90 - 10x + x

= 90 - 9x

When digits are reversed, x becomes the tens digit and (9 - x) becomes the units digit.

Reversed Number = 10(x) + (9 - x)

= 10x + 9 - x

= 9x + 9

The problem states that adding 27 to the original number results in the reversed number.

Original Number + 27 = Reversed Number

(90 - 9x) + 27 = 9x + 9

⇒ 117 - 9x = 9x + 9

⇒ 117 - 9 = 9x + 9x $\quad$ [Transposing -9x to RHS and +9 to LHS]

⇒ 108 = 18x

⇒ x = $\dfrac{108}{18}$

⇒ x = 6

Units digit = x = 6

Tens digit = (9 - x) = (9 - 6) = 3

∴ The original number is 36.

Hence, option 1 is the correct option.