-1

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?

JonathanZ
  • 10,615
lylehunder
  • 1
  • I can only imagine that each stack goes to its own tray, so we are really looking for the smallest stacks/the largest number of trays. Otherwise, taking your position to the extreme, the solution would be $1$ stack, not $2$. –  Apr 26 '23 at 03:08
  • 10 is the number of barfis in each stack, not the number of stacks. – JonathanZ Apr 26 '23 at 03:12
  • dear Stinking Bishop- I also thought it to be 1 stack, but then i realised the question asked for the number of sweets in each stack to be equal to each other. Grammatically this implies that there has to be more than one stack, unless this sentence is valid- "the number of sweets in this stack is equal to each other".

    dear JonathanZ- thank you for your correction. I have made the necessary changes to the question

     – lylehunder Apr 26 '23 at 03:26

1 Answers1

1

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.

JonathanZ
  • 10,615
  • @lylehunder - Can you let me know if this resolves your question? And if you think it's the best answer, you can also click the check mark to show that you've accepted it. – JonathanZ Apr 26 '23 at 18:46
  • Im afraid my question is not resolved. The number in each kaju stack is not meant to be equal to the number in each badam stack. I wanted to know why 2 stacks is not the correct answer. – lylehunder Apr 27 '23 at 09:55
  • Thank you for replying. Me, I think you are misunderstand the question, as it says "each stack has the same number of sweets", and not "each stack has the same number of sweets as the other stacks of its type". I suggest you ask the person who set the question which was intended. – JonathanZ Apr 27 '23 at 15:01
  • Additionally, your solution makes a total of 4 stacks. Why not 2 stacks total, with 275 barfis in each? – JonathanZ Apr 27 '23 at 15:04
  • 2 stacks with 275 barfis each would mean that each stack would have some kaju barfis and some badam barfis. This is not allowed. Each stack must only have one kind of sweet. This question was a part of my textbook which is authored by a government institution called the NCERT. I could write a letter to them but it doesn't guarantee a reply – lylehunder Apr 28 '23 at 05:22
  • "Each stack must only have one kind of sweet". That is not stated anywhere in the problem, but is a condition you have come up with. Admittedly, "kaju stacks must be the same height as badam stacks" is a condition I have come up with, but it is a fairly common sense one, plus it is the only one so far that makes the answer that is given make sense. – JonathanZ Apr 28 '23 at 15:13