I forgot my previous apple ID from which I purchased applications from App Store. How can I update apps as I am unable to do it with my new apple ID?

See if you can recover the ID/password.

Apple ID - How to find your Apple    An iCloud e-mail address is an Apple ID.

Apple ID - Find              

Enter the Apple (iCloud) ID and click Forgot Password.

Apple ID - Manage            

Apple ID – Forgot Password            

One option is to delete the apps/purchases made by the other ID and download them using the new ID if desired. If necessary, check your purchases history to see which apps/purchases weren’t made by the current ID. 

Purchase History Review.   

Or if you can recover the old ID, you can try to set up Family Sharing  between the IDs to keep access to your purchases.

Family Sharing.         

Family Sharing - Set up.