百分數與變分

Suppose $x$ varies directly as $y$ and inversely as $z$. When $y=2$ and $z=3$, $x=7$. When $y=6$ and $z=7$, $x=$

Shop A offers a $10\%$ discount on a book marked at $\$P$. Shop B offers a $15\%$ discount on the same book marked at $\$Q$. If the selling price of the book is the same in both shops, express $Q$ in terms of $P$.

The length of a rectangle is decreased by $20\%$. If the area remains unchanged, find the percentage increase of its width.

The following table shows the compositions of Tea A and Tea B which are mixtures of Chinese tea and Indian tea:

$\begin{array}{|c|c|}\hline & \text{Ratio of Chinese tea and Indian tea by weight}\\\hline\text{Tea A} & 3:1\\\hline \text{Tea B} & 2:3\\\hline\end{array}$

If $4\text{ kg}$ of tea A and $10\text{ kg}$ of tea B are mixed, find the ratio of Chinese tea and Indian tea in the mixture.

$x$ and $y$ are two variables. The table below shows some values of $x$ and their corresponding values of $y$.

Which of the following may be a relation between $x$ and $y$ ?

Find the interest on $\$P$ at $r\%$ p.a. for $n$ years, compounded half-yearly.

The marked price of a toy is $\$120$ and the percentage profit is $60\%$. If the toy is sold at a discount of $20\%$, the profit is

Mr. Chan bought a car for $\$143\,900$. If the value of the car goes down by $10\%$ each year, find its value at the end of the third year. (Give your answer correct to the nearest hundred dollars.)

A wholesaler sells an article to a retailer at a profit of $20\%$. The retailer sells it to a customer for $\$3\,600$ at a profit of $\$720$. Find the original cost of the article to the wholesaler.

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