In a school hall, there were $$65$$ fewer boys than girls. After~$\tfrac{2}{5}$~of the boys and~$\tfrac{3}{7}$~of the girls left the hall for recess, there were equal number of boys and girls that remained in the hall. Find the total number of students that remained in the hall in the end. 
Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization->Equalizing products by Grouping