How to check a datetime duration exists in another datetime duration?

I am developing a Rails application for Examination management.

Exams can be created for a time period.

Exam model have the fields start_date:datetime and end_date:datetime

Exam creation is a 2 step process. In the first step all the exam details including start_date and end_date is given.

In the second step I want to list all exams that have a conflicting time period with the current exam so that the user can choose whether to continue or not.

Example:

Current exam:

Start date and time: "2015-02-23 10:30:00"

End date and time: "2015-02-23 13:30:00"

Conflicting exam:

Start date and time: "2015-02-23 12:30:00"

End date and time: "2015-02-23 14:30:00"

How is it possible?