In appreciation of the social improvements completed in a town, a wealthy philanthropist decided to gift Rs $$750$$ to each male senior citizen in the town and Rs $$1000$$ to each female senior citizen. Altogether, there were $$300$$ senior citizens eligible for this gift. However, only $$8/9$$^th of the eligible men and $$2/3$$^rd of the eligible women claimed the gift. How much money (in Rupees) did the philanthropist give away in total?

If $$pqr \ne 0$$ and $${p^{ - x}} = {1 \over q},{q^{ - y}} = {1 \over r},\,{r^{ - z}} = {1 \over p},$$ what is the value of the product $$𝑥𝑦𝑧$$?

In a party, $$60\% $$ of the invited guests are male and $$400\% $$ are female. If $$80\% $$ of the invited guests attended the party and if all the invited female guests attended, what would be the ratio of males to females among the attendees in the party?

Six people are seated around a circular table. There are at least two men and two women. There are at least three right-handed persons. Every woman has a left-handed person to her immediate right. None of the women are right-handed. The number of women at the table is :