Question: "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 of sweets, 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?"
the smallest possible number of stacks will take the up the least area
They say that the solution is to take HCF of 420 and 130, which is 10. Apparently, 10 sweets in each stack gives the smallest number of stacks Each stack has the same number of sweets: 10 kaju barfis in each of the 42 stacks of kaju barfis, and 10 badam barfis in each of the 13 stacks of badam barfis
But if we ignore the HCF method, logically speaking, the least number of stacks would be 2. In this case, Each stack still has the same number of sweets: 210 kaju barfis in each of the 2 stacks of kaju barfis,and 65 badam barfis in each of the 2 stacks of badam barfis. Perhaps this would not be practically possible in real life, but it fits the criteria given in the question, doesn't it?
Answer to the originally posted version of the question: 10 is the number of barfis in each stack, not the number of stacks.
Answer to the edited version: I think that the number in each kaju stack is supposed to be the same as the number in each badam stack.
Also: the statement of the question is a little bit redundant. Once they say "least area of the tray", that already implies you want to maximize the number of barfis in each stack.