The following problem seems somehow critical to me. The answer of the following question is 10.8 and 8.8.

Two liquids are mixed in the ratio 3:2 and the vendor gains 10% by selling the mixture at 11 USD (US Dollar) per liter. If the first liquid costs 2 USD more than the second, find the cost price of each of the liquids.

To solve this problem the ratio 3:2 was reversed into 2:3, and 2 USD was divided according to this ratio (2:3). In a lecture the solution of this problem was explained, but it explained this solution in such a way that only an expert will realize what lecturer of that video lecture was trying to say. Dividing USD 2 according to 2:3, 0.8 and 1.2 ware derived....and than in a complicated way this problem was solved. But the lecturer of that video lecture claimed that if anybody would follow the way he had showed will be able to solve this sort of problem within a couple of moments.

Please let me know why 3:2 was reversed into 2:3, and by which rule we can divide 2 USD into 0.8 and 1.2 according to the reversed ratio 2:3.