In a two-digit number, the unit digit is 3 more than the ten's digit. The difference between the number and the number formed by interchanging the digits of the number is 27. What is the value of the original number?

Given:

Let's say the ten's digit is x and the unit digit is y.

So according to the question,

y - x = 3 ......(1)

And the number is 10x + y.

If the digits are swapped, then the number will be = 10y + x

So 

The difference will be = (10y + x) - (10x + y) = 9y - 9x

9y - 9x = 27

⇒ y - x = 3 ......(2)

From (1) and (2), we can't determine the value of x and y.

So the answer will be "can't determine".

∴ Option (4) is the correct answer.