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

The price of petrol went up by $20 \%$. In order to keep expenses the same,Ram must reduce travel by: (in $\%$)

What is the $40 \%$ of $50 \%$ of $\frac{3}{4}$ of $3200$?

In Convent Model School,$60 \%$ of the students are boys. In an aptitude test,$80 \%$ of the girls scored more than $40$ marks (out of a maximum possible $150$ marks). If $60 \%$ of the total students scored more than $40$ marks in the same test,find the fraction of the boys who scored $40$ marks or less?

$75 \%$ of $480 = x \times 15$. Find the value of $x$.

If the price of gold increases by $30 \%$,find by how much the quantity of ornaments must be reduced so that the expenditure may remain the same as before?