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A tin is full of wine. Out of this tin, 4 gallons of wine

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

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Answer:28 gallons.

This problem has been solved with a weird formula. Can someone explain how to approach such problems
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Anichka
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Re: Proportional division [#permalink] New post   26 Nov 2012, 14:10
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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.
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A tin is full of wine. Out of this tin, 4 gallons of wine [#permalink] New post   01 Jun 2015, 21:44
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vinubalan wrote:
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.

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Answer:28 gallons.

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


\(36/49 = \frac{100}{100} * [\frac{(V - 4)}{V}]^2\)

\(\frac{V - 4}{V} = \frac{6}{7} = \frac{24}{28}\)

So V = 28

The logic of this formula has been discussed in detail here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/01 ... -mixtures/
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Re: Proportional division [#permalink] New post   24 Mar 2010, 07:16
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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.
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Re: A tin is full of wine. Out of this tin, 4 gallons of wine [#permalink] New post   07 May 2016, 11:33
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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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A tin is full of wine. Out of this tin, 4 gallons of wine [#permalink] New post   01 Jun 2015, 21:17
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Hi All,

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.

GMAT assassins aren't born, they're made,
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Re: A tin is full of wine. Out of this tin, 4 gallons of wine [#permalink] New post   09 Mar 2022, 05:14
Let,
The total quantity of wine in Tin Tank = x gallons
Quantity of wine taken out = 4 gallons
This means we are taking out = \(\frac{4}{x}\) gallons of mixture each time

Quantity of wine remaining in tank each time we take out 4 gallons of mixture = \(1-\frac{4}{x}\) = \(\frac{x-4}{x}\)

Final quantity of wine remaining in tank after repeating it twice = \(x*(\frac{x-4}{x})^2\) = \(\frac{36}{49}\)

\(\frac{x-4}{x}\) = \(\frac{6}{7}\)

x = 28
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Re: A tin is full of wine. Out of this tin, 4 gallons of wine [#permalink] New post   17 Mar 2022, 17:30
Here it is with an explanatory pic:
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Re: A tin is full of wine. Out of this tin, 4 gallons of wine [#permalink] New post   11 Sep 2023, 18:46
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