Hi,
I already have developed a similar but small Web application for my own need. I conduct small online exam in my locale.
I believe it will be a good base for your project with my existing application. Only I have to modify a bit and add new features to my existing code.
I can show you a demo of my current similar project.
Your mentioned budget is not enough for the amount of work needed to be done. So I have bid with a price which I can justify upon discussion.
Hope to hear from you soon.
Thanks,
Shankar