If the digits of a two-digit number are interchanged , the number formed is greater than the the original number by 45. If the difference between the digits is 5, then what is the original number?

Let us assume the two digits number of the number is a and b.
According to given question,
The original number is 10a + b.
After interchanging the digits , the Number is 10b + a.
The number formed is greater than the the original number by 45,
We will get,
New number = Original number + 45
⇒ 10b + a = 10a + b + 45
⇒ 10b + a - 10a - b = 45
⇒ 9b - 9a = 45
⇒ b - a = 5
According the question the difference between the digits is 5 which will not help us to solve this question because both condition given in question are same. So can't be determined the answer.
Now try Hit and Trail method
Try one by one all option. All 3 Options are true.
But we cannot choose all 3 option, but as per question we cannot find the answer.