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From a container of milk, which contains 200 liters of milk, the seller replaces each time with water when he sells 40 liters of milk(or mixture). Every time he sells out only 40 liters of milk(or mixture). After replacing the milk with water 4th time, the total amount of water in the mixture is

Question

From a container of milk, which contains 200 liters of milk, the seller replaces each time with water when he sells 40 liters of milk(or mixture). Every time he sells out only 40 liters of milk(or mixture). After replacing the milk with water 4th time, the total amount of water in the mixture is

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Solution

The problem can be solved step by step as follows:

Step 1: The seller sells 40 liters of milk from the 200 liters, leaving 160 liters of milk. He then adds 40 liters of water, making the mixture 160 liters of milk and 40 liters of water.

Step 2: The seller sells another 40 liters of the mixture. Since the mixture is 80% milk and 20% water, he sells 32 liters of milk and 8 liters of water, leaving 128 liters of milk and 32 liters of water. He then adds 40 liters of water, making the mixture 128 liters of milk and 72 liters of water.

Step 3: The seller sells another 40 liters of the mixture. Now, the mixture is approximately 64% milk and 36% water, so he sells about 25.6 liters of milk and 14.4 liters of water, leaving about 102.4 liters of milk and 57.6 liters of water. He then adds 40 liters of water, making the mixture about 102.4 liters of milk and 97.6 liters of water.

Step 4: The seller sells another 40 liters of the mixture. Now, the mixture is approximately 51% milk and 49% water, so he sells about 20.4 liters of milk and 19.6 liters of water, leaving about 82 liters of milk and 78 liters of water. He then adds 40 liters of water, making the mixture about 82 liters of milk and 118 liters of water.

So, after replacing the milk with water for the 4th time, the total amount of water in the mixture is approximately 118 liters.

This problem has been solved

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