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 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?

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 :

The expression $\frac{(x+y)-|x-y|}{2}$ is equal to :