Option 2 : 74

**Given:**

Sum of digits of a two digit number is 11.

**Concept used:**

A two digit number can be written as (10 × tenth place digit) + unit digit

**Calculation:**

Let unit digit and tenth digit of the number be x and y respectively

So, x + y = 11 ----(1)

And, number will be 10y + x ----(2)

When we reverse these digits, then unit digit be y and tenth place digit be x.

Then the new number will be 10x + y ----(3)

According to the question, we have

⇒ (10y + x) - (10x + y) = 27

⇒ 9y - 9x = 27

⇒ 9y - 9x = 27

⇒ 9(y - x) = 27

⇒ y - x = 3 ----(4)

Now add equation (1) and equation (4), we get

⇒ 2y = 14

⇒ y = 7 ----(5)

Put value of equation (5) in equation (1), we get

⇒ x + 7 = 11

⇒ x = 4

So, Original number = (10 × 7) + 4

⇒ 70 + 4

⇒ 74

**∴ The original number is 74.**

__Shortcut Trick__

Go through the options and check which one satisfies the given question.

Here in option (2) we have

7 + 4 = 11

and difference of reversed digit number = 74 - 47

⇒ 24

Which satisfies the given question

∴ The original number is 74.