How does sololearn manages the expenditure of servers and related things if it is free to use?

Answer 1

Through partnerships and mini-ads inserted sometime in the home page, just trying to guess... it remains one of the biggest secrets in the world.

Answer 2

There are some champion donaters in the world. Bill Gates for instance is one of the key angel investors and has donated at last count 11 million to Khan academy for instance. Big money on silicon valley for good concepts.