Once you have done a lot of problem interviews you should be getting a better understanding of the problem but what is the job that actually needs to be done to solve the problem?
The job someone wants done is much more important than who the person is
To understand the difference between problems and jobs think about the last time you went to the doctor. You may have said "Doc, I have a sore back" - that is the problem, you are an expert at it because you are the one experiencing it. If the doctor asked you "So, what do you think we should do about it?", you would probably say "I don't know but it hurts can I have some pain killers?". Turns out the job to be done is to fix your Abdominal Aortic Aneurysm and the solution is surgery.
With this in mind categorising any of your target markets by their demographics or psychographics is crazy. What you need to do is understand the situation that they are in which brings about the motivation to get the job done. From there you can start to think about who else is in that same situation and therefore might have the same job to be done.
You can glimpse a solution by identifying the job which can only come from understanding the problem. People are experts in their problems but often don't realise the actual job they need to be done and therefore have little insight about what the correct solution could be.
Once you have the job that needs to be done you can represent that as a value proposition, which is a statement describing the benefits or outcomes that customers expect to receive from your product or service.
This statement should get across the 'why' behind purchasing.