$15 \%$ of $10 \%$ of $20 \%$ of $1000$ is?

If $x$ $\%$ of $y$ is $100$ and $y$ $\%$ of $z$ is $200,$ then find a relation between $x$ and $z$.

$405$ toffees were distributed equally among children in such a way that the number of toffees received by each child is $20 \%$ of the total number of children. How many toffees did each child get?

$1200$ boys and $650$ girls appeared in an examination. If $70 \%$ of boys and $40 \%$ of girls failed,find the approximate percentage of passed students.

Sixty-five percent of a number is $21$ less than four-fifth of that number. What is the number?

If all sides of a hexagon are increased by $7 \%$,find the percentage increase in its area. (in $\%$)