Explanation:

From I: Let the required number be (10x+y).
Now, 10x + y = 10y + x + 27
=> (x – y) = 3
So, the possible values of x and y are 96,85,74,63,52 and 41.
We cannot find an unique solution.
So, this statement is not alone to solve the question.
From II: Two-digit numbers which are multiple of 9 = 18,27,36,45,54,63,72,81,90,99
We cannot find unique solution.
So, this statement alone is not sufficient.
Combining both the equations. Let the required number be (10x+y).
10x + y = 10y + x + 27
=> (x – y) = 3
So, the possible values of x and y are 96,85,74,63,52 and 41.
Two-digit numbers which are multiple of 9 = 18,27,36,45,54,63,72,81,90,99.
So, 63 is the required two-digit number.
So, the factors of 63 are 1,3,7,9 21,63.
Both are necessary to answer.

Hence, option 5 is the correct answer.