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

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A tin is full of wine. Out of this tin, 4 gallons of wine [#permalink]  24 Mar 2010, 05:58
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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.

[Reveal] Spoiler:

This problem has been solved with a weird formula. Can someone explain how to approach such problems
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Re: Proportional division [#permalink]  24 Mar 2010, 06:16
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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: Proportional division [#permalink]  26 Nov 2012, 13:10
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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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Re: A tin is full of wine. Out of this tin, 4 gallons of wine [#permalink]  16 Dec 2013, 06:39
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Re: A tin is full of wine. Out of this tin, 4 gallons of wine [#permalink]  01 Jun 2015, 07:23
Hello from the GMAT Club BumpBot!

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A tin is full of wine. Out of this tin, 4 gallons of wine [#permalink]  01 Jun 2015, 20:17
Expert's post
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.

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A tin is full of wine. Out of this tin, 4 gallons of wine [#permalink]  01 Jun 2015, 20:44
Expert's post
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.

[Reveal] Spoiler:

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: http://www.veritasprep.com/blog/2012/01 ... -mixtures/
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A tin is full of wine. Out of this tin, 4 gallons of wine   [#permalink] 01 Jun 2015, 20:44
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