百分數與變分

Let $x$ vary inversely as $\sqrt y$. If $y$ is increased by $69\%$, then $x$ will be

The price of a cylindrical cake of radius $r$ and height $h$ varies directly as the volume. If $r=5\text{ cm}$ and $h=4\text{ cm}$, the price is $\$30$. Find the price when $r=4\text{ cm}$ and $h=6\text{ cm}$.

A merchant marks his goods 25% above the cost. He allows 10% discount on the marked price for a cash sale. Find the percentage profit the merchant makes for a cash sale.

If $a:b=2:3$ and $b:c=5:3$, then $\dfrac{a+b+c}{a-b+c}=$

Which of the following gives the compound interest on $\$10000$ at $6\%$ p.a. for one year, compounded monthly?

Originally $\dfrac{2}{3}$ of the students in a class failed in an examination. After taking a re-examination, $40\%$ of the failed students passed. Find the total pass percentage of the class.

If $\dfrac{a}{b}=\dfrac{c}{d}=k$ and $a,b,c,d$ are positive, then which of the following must be true?

If $a:b=2:3$, $a:c=3:4$ and $b:d=5:2$, find $c:d$.

Suppose $x$ varies directly as $y^2$ and inversely as $z$. Find the percentage increase of $x$ when $y$ is increased by $20\%$ and $z$ is decreased by $20\%$.

A sum of $\$10\,000$ is deposited at $4\%$ p.a., compounded yearly. Find the interest earned in the second year.