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A milkman starts with a 100 liter can of pure milk from his dairy and he sells 10 liters of it to the first customer, then he adds 10 liters of water. After this, he sells 10 liters each to two customers and adds 20 liters of water. After this, he sells 10 liters each to three customers and adds 30 liters of water. Thus, every time he dilutes the mixture he sells it to one more customer than before and he keeps on replacing the mixture sold with water. In this way how many customers get at least 50% milk in the mixture that they purchase from this milkman

Question

A milkman starts with a 100 liter can of pure milk from his dairy and he sells 10 liters of it to the first customer, then he adds 10 liters of water. After this, he sells 10 liters each to two customers and adds 20 liters of water. After this, he sells 10 liters each to three customers and adds 30 liters of water. Thus, every time he dilutes the mixture he sells it to one more customer than before and he keeps on replacing the mixture sold with water. In this way how many customers get at least 50% milk in the mixture that they purchase from this milkman

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Solution

To solve this problem, we need to keep track of the amount of milk and water in the can after each transaction.

  1. Initially, the milkman has 100 liters of pure milk. He sells 10 liters to the first customer, who therefore gets 100% milk. The milkman then adds 10 liters of water, leaving him with 90 liters of milk and 10 liters of water.

  2. The milkman sells 10 liters each to two customers. Since the mixture is 90% milk and 10% water, each customer gets 9 liters of milk and 1 liter of water, which is 90% milk

This problem has been solved

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