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.

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:

http://www.veritasprep.com/blog/2012/01 ... -mixtures/
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Karishma

Veritas Prep GMAT Instructor

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