Question

A school has 9 periods a day each of 40 minutes duration. How long would each period be, if the school has 8 periods a day, assuming the number of school hours to be the same?

Answer 1

Let x min be the duration of each period when the school has 8 periods a day.

No. of periods	9	8
Time (in min)	40	x

Clearly, if the number of periods reduces, the duration of each period will increase.
So, it is a case of inverse proportion.
$$\begin{gathered} \mathrm{Now},9\times 40=8\times x \\ \Rightarrow x=\frac{9\times 40}{8} \\ \Rightarrow x=45 \end{gathered}$$

Therefore, the duration of each period will be 45 min if there were eight periods a day.