Question

A batch of bottles were 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

Hint: To solve the given question, we must note down the given data and we know that the size of the box depends with respect to size of bottles, hence based on the quantity of bottles we can find in how many boxes 20 bottles can be packed and let us consider x to be the number of boxes to find.

Complete step-by-step answer:
25 boxes are packed with 12 bottles in each box; hence we need to find the number of boxes if 20 bottles are in each box.
Let x be the number of boxes.
The following table is obtained:

Number of boxes	25	x
Number of bottles in each box	12	20

As we increase the number of bottles in each box, the number of boxes to be packed decreases. Therefore, they are in inverse proportion.
Hence, now let us find the number of boxes required to pack these bottles as: \[\left( {{x_1}{y_1} = {x_2}{y_2}} \right)\]
\[25 \times 12 = x \times 20\]
\[\dfrac{{25 \times 12}}{{20}} = x\]
\[\dfrac{{5 \times 12}}{4} = x\]
\[5 \times 3 = x\]
Hence, the value of x is:
\[x = 15\]
Therefore, the number of boxes required to pack these bottles is 15.
So, the correct answer is “ 15 ”.

Note: The key point to solve this given question is that as mentioned 25 boxes with 12 bottles in each box, it implies that more the number of bottles, lesser will be the number of boxes. Hence, the number of bottles and the number of boxes required to pack these are inversely proportional to each other and obtaining the table we can solve these types of questions easily.