In a class,~$\tfrac{1}{4}$~of the students and an additional $$3$$ boys like badminton.~$\tfrac{1}{3}$~of the remaining students in the class less $$3$$ like table tennis and the rest of the $$25$$ students in the class like football. How many students are there in the class? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems