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?

Answer 1

Finding the number of boxes:

Let the number of boxes be $\text{a}$.

Number of bottles in each box	$12$	$20$
Number of boxes	$25$	$\text{a}$

Thus, The number of bottles and the number of boxes are inversely proportional.

Therefore, from inversely proportional property, we get

$\begin{array}{rcl}{\text{x}}_1{\mathrm{y}}_1& =& {\mathrm{x}}_2{\mathrm{y}}_2\\ 12\times 25& =& 20\times \mathrm{a}\\ \mathrm{a}& =& \frac{12\times 25}{20}\\ \mathrm{a}& =& 15\end{array}$

Hence, the number of boxes would be filled is $15$.