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The volumes of two vessels, which are filled up to the brim by milk of different prices, are 220 L and 180 L. An equal amount of milk is taken out from each of the two vessels, and the milk taken out from the first vessel is poured into the second vessel while the milk taken out from the second vessel is poured into the first vessel. If the price per liter of milk in both the vessels becomes the same eventually, find the volume of milk taken out from each of the two vessels.
Let the concentrations be a and b respectively. Let x be the quantity interchanged.
Volume of milk in the first container after the exchange = a/100 * (220-x) + bx/100
Proportion of milk = 1/220 * [a/100 * (220-x) + bx/100]
Similarly, proportion of milk in the second container after exchange = 1/180 * [b/100 * (180-x) + ax/100]
These two are equal
Solving the equality, we get x = 99 L
