The sum of the digits of a two digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is

1. 27

2. 72

3. 63

4. 36

Let the digit at ten's place be x and digit at one's place be y.

Given, sum of digits = 9.

⇒ x + y = 9 …….(i)

Number = 10 × x + y = 10x + y

On reversing digits, number = 10 × y + x = 10y + x.

⇒ 10x + y + 27 = 10y + x

⇒ 10x - x + y - 10y + 27 = 0

⇒ 9x - 9y + 27 = 0

⇒ 9(x - y + 3) = 0

⇒ x - y + 3 = 0

⇒ y - x = 3 …….(ii)

Adding (i) and (ii) we get,

⇒ x + y + (y - x) = 9 + 3

⇒ 2y = 12

⇒ y = 6.

Substituting value of y in (i) we get,

⇒ x + 6 = 9

⇒ x = 3.

Number = 10 × x + y = 10 × 3 + 6 = 36.

Hence, Option 4 is the correct option.