Licensing Methods Used In Open-Source Softwares.

Nope, you don't have to pay for modifying the source-code.
under GPLv2,You don't even have to pay the original developer for selling the modified the source-code, what you have to do is to give same right to whom you're selling & include that it's not solely developed by you & add the original developers identity.

Discussing about opensource licensing is quite a deep-talk. There are many license GPLv1 to GPLv3, BSD License.None of the licensing methods are focused on earning profit, infact it is very much focused on the objective that the original developer's work doesn't get misused.However in BSD license, there is simply no rule, anyone can use original source-code licensed under BSD, customize it & sell it even without mentioning original developers name in it which is not good IMO, but this is how this license works & thus no current generation developers licenses their work under BSD, rather they prefer GPLv2 which is quite an awesome license. (That's reason why mac OS X which uses FBSD stacks is there & the only reason why Sony uses BSD instead of Linux)

How they earn profit ?
Well, if the opensource project is impressive & any company is interested then the company pays the original developer to continue it's development & improve the software.
Eg : Linux kernel. It's backed by Google, Intel, IBM & many other giants. Thus even after 20 years of Linux, it's development haven't stopped.

Thanks Abhishek.
Yes you are correct discussing on open source is deep-talk and understanding it too.

Thanks lots of information😀👍