Bunuel wrote:

A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?

A. 2:5

B. 3:5

C. 2:3

D. 3:2

E. 5:3

The original mixture has a ratio of milk to water = 3x : 2x, and thus:

40 = 5x

x = 8

So, originally there were 3(8) = 24 liters of milk and 2(8) = 16 liters of water.

Since 20 liters of the mixture (i.e., half of the mixture) are removed, half of the milk (12 liters) and half of the water (8 liters) are removed. Thus, after 20 liters are removed, there are:

12 liters of milk and 8 liters of water in the mixture.

Since 20 liters of milk are added back in, we now have:

32 liters of milk and 8 liters of water in the mixture.

Since another 20 liters of the mixture (i.e., half of the mixture) are removed, half of the milk (16 liters) and half of the water (4 liters) are removed. Thus, after 20 liters are removed, there are:

16 liters of milk and 4 liters of water in the mixture.

Since 20 liters of water are added back in, we now have:

16 liters of milk and 24 liters of water in the mixture.

Thus, the final ratio of milk to water is 16/24 = 2/3.

Answer: C

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