Backend development of any project usually takes 2-6 weeks. Specifically, if your app/web concept is simple, the back-end will take less time, but if the number of screens is more and the app/web is based on high-complexity features & functionalities, then the back-end development will take longer time.
The duration to do the back end will also depend on the developer’s skill set & experience. If the back-end developer is amateur, it will take longer, and if you have a back-end expert to back your project, it will take less time to do the background work.
It all depends! :)