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

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## 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.

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