# Ex.13.2 Q7 Direct and Inverse Proportions Solution - NCERT Maths Class 8

## Question

A batch of bottles was packed in \(25\) boxes with \(12\) bottles in each box. If the same batch is packed using \(20\) bottles in each box, how many boxes would be filled?

## Text Solution

**What is Known?**

\(25\) boxes were packed with \(12\) bottles in each box.

**What is Unknown?**

No. of boxes when \(20\) bottles are packed with each box.

**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.

\[{x_1}{y_1} = {x_2}{y_2}\]

**Steps:**

If the no. of bottles in each box increases, no. of boxes will decrease. Hence, it is Inverse proportion.

\[\begin{align}{x_1}{y_1} &= {x_2}{y_2}\\12 \times 25 &= 20 \times {y_2}\\{y_2} &= \frac{{12 \times 25}}{{20}}\\{y_2} &= 15\end{align}\]

Hence \(15\) boxes will be filled with \(20\) bottles in each box.