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

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## 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.

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