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

An agent sells goods of value of Rs. $15000$. The commission which he receives is $12 \frac{1}{2} \%$. What is the commission amount?

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

An army lost $10 \%$ of its men in war,$10 \%$ of the remaining died due to disease,and $10 \%$ of the rest were declared disabled. Thus,the strength of the army was reduced to $7,29,000$ active men. What was the original strength of the army?

In a class,$60 \%$ of the students pass in Hindi and $45 \%$ pass in Sanskrit. If $25 \%$ of them pass in both subjects,what percentage of the students fail in both subjects?

In Mumbai,$60 \%$ of the registered voters are $BJP$-supporters and the rest are Congress-supporters. In a mayoral race,if $75 \%$ of the registered voters who are $BJP$-supporters and $20 \%$ of the registered voters who are Congress-supporters are expected to vote for candidate $X$,what percent of the registered voters are expected to vote for candidate $X$?