Use another AppleID in iOS 7.1.2 AppStore?
You need to update the app using the Apple ID it was installed with. 

For example, say if I install app A with Apple ID B, then sign out and in using Apple ID C, to update app A I need to use Apple ID B.

The most optimal solution to this is re-installing the app on the new Apple ID after saving snaps backing up any data.

From the comments:


  Note that this may require paying for apps and in-app purchases again. You can avoid this in some (but not all) cases by setting up family sharing between the two Apple IDs.