# Ex.13.2 Q11 Direct and Inverse Proportions Solution - NCERT Maths Class 8

## Question

A school has \(8\) periods a day each of \(45\) minutes of duration. How long would each period be, if the school has \(9\) periods a day assuming the number of school hours to be the same?

## Text Solution

**Reasoning:**

Two numbers *\(x\)* and *\(y\)* are said to vary in inverse proportion if

\[\begin{align}xy = {\rm{ }}k,{\rm{ }}x{\rm{ }} = {\rm{ }}\frac{1}{y}k\end{align}\]

Where* \(k\)* is a constant.

\[\begin{align}{x_1}{y_1} = {x_2}{y_2}\end{align}\]

**What is Known?**

\(8\) periods of day each of \(45\) min.

**What is ****Unknown?**

\(9\) periods in a day, how many minutes each period will be?

**Steps:**

If the number of period increase, then the duration of the period will decrease. So, it is inverse variation.

\[\begin{align}{x_1}{y_1} &= {x_2}{y_2}\\8 \times 45 &= 9 \times {y_2}\\{y_2} &= \frac{{8 \times 45}}{9}\\{y_2} &= 40\end{align}\]

Hence, each period would be \(40\) minutes long.