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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] New post 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:
Answer:28 gallons.

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] New post 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] New post 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] New post 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] 16 Dec 2013, 06:39
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