More Coffee or Tea? #2
Take 1 teaspoon of coffee from a cup of coffee and empty it into a cup of tea. Stir the tea. Take 1 teaspoon from the teacup and empty it into the coffee cup. Stir.
Is there more coffee in the teacup or tea in the coffee cup?
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6 solutions
Let there be 10x coffee in the coffee cup and 10y tea in the tea cup
After transfer 1 : 9 x and 1 0 y + x
After transfer 2 : 9 x + 1 1 1 ( 1 0 y + x ) and 1 1 1 0 ( 1 0 y + x )
Note that both y in coffee cup and x in tea cup are equal.
I got it wrong anyway... Didn't think that tea cup had more :)
To be honest let's just say that since both volumes in each cup remains the SAME and are EQUAL, then obviously there has to be the same amount of tea in the coffee cup as the amount of coffee in the tea cup, since no coffee or tea was externally introduced throughout the procedure.
Write a comment or ask a question... but in question they have given that "one teaspoon from teacup " but not one teaspoon of tea from teacup :(
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@Ayan Bhuyan the teaspoon can only hold 10 particles, and also for @Rishabh Goyal the teaspoon is full, which means only 10 particles of each substance are transferred with the spoons.
@Kevin Patel : Because you had it wrong? :P
@Niranchana Gopi good one.
Thats...the nice way to solve hehehe
no but cofee is more dense so more particles will come in as compared to tea
Answers: coffee should be more.
I thought the same but won't the density of the tea change even if by a small amount, which makes it impossible to actualy say how many particles you take from the cup of tea? It may be 11 or 12..
Now I got it! Thank you for the explanation
nice explanation
well
well explained..
Oh my God! You are from Leiden. (Okay, this is not connected to your solution.)
Let the amount of coffee in the cup of tea be x . Thus, we have x units of coffee missing from the cup of coffee. Since the amount of liquid in each cup is the same, we must have that the x missing units was replaced by tea. Thus, there is the same amount of coffee and tea in the tea and coffee cups.
In other words, what coffee that isn't in the coffee cup must be in the tea cup, and what tea not in the tea cup is in the coffee cup; since the amount of liquid in the two cups before and after the exchange is the same, the amount of coffee replaced by tea is the same as the amount of tea replaced by coffee.
I thought that while putting 1 teaspoon of tea in the coffee cup, there might have been a very small amount of coffee with tea......... which made my answer wrong
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It doesn't matter how much coffee will come with the teaspoon of tea. Even if the teaspoon from the tea to the coffee consists entirely out of coffee, the answer would still be "They are both equal" (as then there would be no tea in the coffee and no coffee in the tea).
i was imagined that as well
But you stir it? So there will be dilution. How sure are we that when you get teaspoon from the teacup with coffee beforehand will be pure tea only? Am i wrong in understanding the problem? Thanks
The initial amounts of coffee and tea does not have to be equal. Does this change your thinking?
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No. It does not matter whether the total amount in each cup is different, the change in amount after the transfers is the same (that is, zero). My reasoning is still sound.
coffee should be more in tea
Let x be the volume of a teaspoon. Let y be the volume of coffee that was returned to the coffee cup. Then x-y represents the amount of coffee in the teacup and x-y also represents the amount of tea placed into the coffee cup.
but when you pick the tea with the spoon, you are also picking a small volume of the coffee that was added before.
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I agree. Then what is your answer?
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I have answered "There's more coffee in the teacup than tea in the coffee cup" but I don't believe it anymore. I think we can't actually be sure if there's more coffee in the teacup or they have the same amounts. A matter of probability perhaps?
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@Vitor da Silva – No probability matter here.
And also the initial amounts do not affect the answer.
Consider 2 containers with 1000 cm^3 of black marbles and 500 cm^3 of white marbles (marbles of equal sizes) and the transfer apparatus which can hold 100 cm^2 of marbles.
Are there more black marbles in the container of white marbles or white marbles in the container of black marbles?
The wording is very specific. It says a teaspoon of the tea, not of the solution of tea and coffee.
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How about "Take 1 teaspoon of liquid from the teacup and empty it into the coffee cup". Does this make any difference in your reasoning? I didn't intend to specify only tea in the 2nd transfer.
no- it says "take one teaspoon from the teacup"- meaning tea and coffee in the teacup
But you stir it? So there will be dilution. How sure are we that when you get teaspoon from the teacup with coffee beforehand will be pure tea only? Am i wrong in understanding the problem? Thanks
let us suppose volume of milk is same in both therefore after the activity volume of milk in both cups will remain same therefore both are equal
Why don't you think the volume of a spoon is the same?
Whatever the density, the volumes you transferred are the same.
so simple one to another another to one are always equal
But the one coming back wasn't pure coffee!
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even though it wasn't pure coffee , some amount of coffee is also present which add to the amount of coffee in the coffee cup.
I think this is the most stupid question I have ever seen.
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Rami, What is your answer then?
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@Guiseppi Butel – The answer is there is more coffee in the tea cup than the amount of tea present in the coffee cup.
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@Rama Devi – Sorry about misspelling your name, Rama, but I believe that your answer is incorrect. Could you substantiate your belief?
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@Guiseppi Butel – Yes.My answer is right because the liquid in the spoon that contains some amount of coffee.Therefore it adds to the amount of coffee in the tea cup.
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@Rama Devi – How could the "some amount of coffee" in the spoon which is emptied into the coffee cup "adds to the amount of coffee in the tea cup."? Explain please!
Do you mean "adds to the amount of coffee in the coffee cup"?.
@Guiseppi Butel – And by the way I am Rama and not Rami
Let's pretend the coffee and tea are particles, and with the teaspoon you take 10 particles from one cup to the other. So, if you take in the first step 10 particles of coffee to the tea, you have a lot of tea particles + the 10 coffee particles. Stir. Then you take 10 particles from the tea. If these are all tea particles, you have 10 particles of coffee in the tea and 10 particles of tea in the coffee. So they're equal. If you take 9 tea particles and 1 coffee particle, 9 coffee particles will remain in the tea and 9 tea particles will be in the coffee. Still equal. This will remain for all other cases, and someone can comment a formula by this, but this was the easiest and most understandable way to express my solution :P