C#

In my interview following question was asked but I was unable to answer. Please help me in solving it.

The algorithm below is a simple checksum formula used to validate a variety of identification numbers.

Your Task: Write a class that can be used to add a check digit to any number.
The check digit is calculated as follows:

1.	Counting from the right-most digit and moving left, double every alternate digit starting with the first one. For any digits that thus become 10 or more, take the two numbers and add them together. For example, 111 becomes 212, while 876 becomes 773.

2.	Add all these digits together. For example, if 111 becomes 212, then 2+1+2 is 5; and 873 becomes 773, so 7+7+3 is 17.

3.	The check digit is: 10 – (<the sum above> % 10), where % is the modulus operator (gives the remainder after division). For example, the check digit for 111 is 10 - the remainder of (2+1+2)/10, which is 5. The check digit for 876 is 10 - (7+7+3)%10, which is 3.

Hi,
I was given following question as an assessment but unfortunately I was unable to answer. Can someone help ?
The question is ;
The function given below is supposed to retrieve the substring between and including the ith and jth characters of the input string s.  When i and j are out of range, ie. i,j< 0 ori,j >= s.length(), the function returns the string "<error>". The following table shows the expected and actual return values of the function for various inputs.

Test case	s	      i	j	Expected return value	Actual return value
1	        "quick"	  0	2	"qui"	                 "qui"
2	        "brown"	  2	1	"ro"	                 ""
3	        "fox"	  1	9	"<error>"	             "<error>"
4	        "jumped"  -1	4	"<error>"	             "<error>"
5	        "lazy"	  3	0	"lazy"	                 "<error>"
6	        "dog"	  1	1	"o"	                     "o"

Unfortunately, the function returns the wrong value for the 2nd and 5th test cases.

C# Version:
string SubString(string s, int i, int j)
{
      int k;
string result;
      try
      {
            k = s.Length;
            if (i < 0 || j < 0 || i >= k || j >= k)
                  throw new Exception();
            result = s.Substring(i, j + 1 - i);
      }
      catch (Exception e)
      {
            return "<error>";
      }
return result;
}
a) Under what general conditions does the function return the wrong value? 
 
b) Add some code to fix the function. Can you improve it? If so explain why your version is better.