$405$ 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?

Five-ninths of a number is equal to $25$ per cent of the second number. The second number is equal to one-fourth of the third number. The value of the third number is $2960$. What is $30$ per cent of the first number?

In an examination,$37 \frac{1}{2} \%$ of the candidates were girls. If $75 \%$ of the boys and $62 \frac{1}{2} \%$ of the girls passed,and $342$ girls failed,find the number of boys who failed.

In an election between two candidates,one got $55 \%$ of the total valid votes,and $20 \%$ of the total votes were invalid. If the total number of votes polled was $7500$,what was the number of valid votes that the other candidate received?

$60 \%$ of $264$ is the same as

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