Question

A sweet seller has $420$ Kaju burfis and $130$ Badam burfis she wants to stack them in such a way that each stack has the same number and same type, and they take up the least area of the tray. What is the number of burfis that can be placed in each stack for this purpose?

Answer 1

The area of the tray that is used up in stacking the burfis will be least if the sweet seller stacks maximum number of burfis in each stack. Since each stack must have the same number of burfis. Therefore, the number of stacks will be least if the number of burfis in each stacks in equal to the

$HCF$ of $420$ and $130$.

In order to find the $HCF$ of $420$ and $130$, let us apply Euclids division lemma to $420$ and $130$ to get
$420=130\times 3+30$

Let us now consider the divisor $130$ and the remainder $30$ and apply division lemma to get
$130=30\times 4+10$

Consider now divisor $30$ and the remainder $10$ and apply division lemma, we get
$30=3\times 10+0$

Since the remainder at this stage is zero. Therefore, last divisor $10$ is the $HCF$ of $420$ and $130$.
Hence , the sweet seller can make stacks of $10$ burfis of each kind to cover the least area of the tray.