A sweet seller has $420$ Kaju barfis and $130$ Badam barfis. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the maximum number of barfis that can be placed in each stack for this purpose?
Step-by-Step Solution
Key Concept: To take up least area, stack size must be maximum $\Rightarrow \text{HCF}(420, 130)$.
Stepwise Solution:
Number of barfis in each stack $= \text{HCF}(420, 130)$. [0.5 Mark]
Prime factorisations:
$420 = 2^2 \times 3 \times 5 \times 7$
$130 = 2 \times 5 \times 13$. [1.5 Marks]
$\text{HCF}(420, 130) = 2 \times 5 = 10$. [1.0 Mark]
Therefore, the sweet seller can make stacks of $10$ barfis each. [0.5 Mark]
Marking Scheme:
• Identifying HCF calculation requirement: 0.5 Mark
• Prime factorisations of 420 and 130: 1.5 Marks
• Evaluating HCF $= 10$: 1.0 Mark
Correct Answer: