As follow up from yesterday, I've uploaded a zip file containing the dtsx package (detailed below) and a folder (containing an A and B file) that should be saved in your local c:\test folder.

File A has four columns and 5 data records, file B has 6 columns and 3 data records.

In a nutshell, the package loops through that SSC_20130507 directory with the two files, parsing them in a single data flow. Using a Delimiter variable (a pipe, in this example) and key values to be found in each file's header, first column ("Col1A" and "Col1B", respectively ... this is shortened to 5 characters from the OP's 10 character request, but demonstrates the functionality) the Data flow determine's each file's type (A or B) based on that key, appends "A" or "B" to the file record, and then conditionally splits the data flow from there. Demonstrating that each file's data can then be parsed and used in its own subsequent set of tasks, a derived column task shreds the column data based on the Delimiter var in to distinct columns, which can then be later used in the data flow (terminating here in Union All transformations, for simplicity).

Basically, while there can be different approaches to handling this problem, including Script Tasks in the control flow, external scripting (PowerShell), etc., I wanted to demonstrate that yes, you can accomplish this fairly easily within a single data flow.