Mixing vinegar and oil
You have two jars. One contains vinegar, the other oil. The two jars contain the same amount of their respective fluid.
Take a spoonful of the vinegar and transfer it to the jar of oil. Then, take a spoonful of liquid from the oil jar and transfer it to the vinegar jar. Stir. Now, how does the dilution of vinegar in the vinegar jar compare to the dilution of oil in the oil jar?
Both are equally dilute.
assumptions: when transferring a mixture of liquids, half a spoon is oil and the other half is vinegar.
consider both jars to initially contain only one spoonful of respective fluid. The dilutions after the process can be easily proved to be equal in both. both jars will have half spoonfuls of oil and vinegar.
if you are not convinced
let both have x ml of liquids.
one spoonful: y ml
After first transfer, jars have (x-y) ml of vinegar and x ml of oil and y ml of vinegar respectively.
After second transfer:
y/2 ml of vinegar and y/2 ml of oil is transferred to jar containing vinegar.
Jars now have:
(x-y/2) ml of vinegar +y/2 ml of oil and (x-y/2) ml of oil +y/2 ml of vinegar.
Therefore, they are equally diluted.
though dilution of oil in vinegar jar is not equal to that of vinegar on oil jar.
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