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A tin is full of wine. Out of this tin, 4 gallons of wine [#permalink]

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24 Mar 2010, 06:58

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A tin is full of wine. Out of this tin, 4 gallons of wine are taken out and 4 gallons of water are added. After this 4 gallons of mixture were taken out and again 4 gallons of water were added. Now the ratio of wine and water in the tin becomes 36:13. Find the volume of tin.

1st stage :A tin is full of wine.Out of this tin, 4 gallons of wine are taken out and 4 gallons of water are added. Wine = w-4 water = 4

2nd stage: After this 4 gallons of mixture were taken out and again 4 gallons of water were added

\(x+y = 4\) where x =\((\frac{{w-4}}{4})*k\) and y = \((\frac{4}{w})k\) ==< proportionate division. add them , we get k = 4. 3rd stage :Now the ratio of wine and water in the tin becomes 36:13.Find the volume of tin.

we have\(\frac{(w-4-x)}{(4-y +4)}\)= \(\frac{36}{13}\)

put the value of x and y we get w =28, it took more than 3 minutes. Such question will not be asked , if its asked calculation will be easy.
_________________

It could be easily calculated with the following approach:

We know wine/water = 36/13, therefore wine to total is 36/(36+13) or 36/49.

Out of the Total amount has been taken 4 gallons of wine, so the ratio of wine to total is (T-4)/T. The wine has been taken out twice, therefore, we put the ratio on a power of two and we make the following equation.

36/49 = ((T - 4)/T)^2

36 and 49 are both powers, so we can square the whole equation reaching the single equation of 6/7 = (T - 4)/T, solving it T=28.

Re: A tin is full of wine. Out of this tin, 4 gallons of wine [#permalink]

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16 Dec 2013, 07:39

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Re: A tin is full of wine. Out of this tin, 4 gallons of wine [#permalink]

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01 Jun 2015, 08:23

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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It's not clear what the source is for this question, but If this question were to appear on the Official GMAT, then it would include 5 ANSWER choices. You could then TEST those answers and find the solution without too much trouble.

A tin is full of wine. Out of this tin, 4 gallons of wine are taken out and 4 gallons of water are added. After this 4 gallons of mixture were taken out and again 4 gallons of water were added. Now the ratio of wine and water in the tin becomes 36:13. Find the volume of tin.

This problem has been solved with a weird formula. Can someone explain how to approach such problems

Multiple replacement questions can be easily handled using this formula:

Cf = Ci * (Vi/Vf)^n

Cf - Final concentration of the element that was NOT added back. This is concentration of wine i.e. 36/49 since ratio of wine:water = 36:13 Ci - Initial concentration of the element that was NOT added back. This 100% since the tin was full of pure wine. Vi - Volume after removal. If volume of tin is V, this is V - 4. Vf - Volume after adding back. This is V n - Number of time the process was repeated. This is 2

Re: A tin is full of wine. Out of this tin, 4 gallons of wine [#permalink]

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07 May 2016, 11:33

Anichka wrote:

It could be easily calculated with the following approach:

We know wine/water = 36/13, therefore wine to total is 36/(36+13) or 36/49.

Out of the Total amount has been taken 4 gallons of wine, so the ratio of wine to total is (T-4)/T. The wine has been taken out twice, therefore, we put the ratio on a power of two and we make the following equation.

36/49 = ((T - 4)/T)^2

36 and 49 are both powers, so we can square the whole equation reaching the single equation of 6/7 = (T - 4)/T, solving it T=28.

This is definitely a faster and easier approach.

it says the mixture was taken out second time then we cant treat the mixture as the wine

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