Problem: Shrewd Milkman

A milkman has a mixture of water and milk in the ratio of 2:3. He wants to remove a part of this mixture and replace it with water so that the new solution contains water and milk in the ratio of 1:1. What part of the mixture should be removed and replaced with water?

Solution:

To solve this problem, we need to follow the given steps:

Step 1: Let us assume that the milkman has 5 liters of the mixture.

Therefore, the amount of milk in the mixture = (3/5) x 5 = 3 liters

And the amount of water in the mixture = (2/5) x 5 = 2 liters

Step 2: Let us assume that 'x' liters of the mixture is removed from the container.

Therefore, the amount of milk in the removed mixture = (3/5) x x = (3x/5) liters

And the amount of water in the removed mixture = (2/5) x x = (2x/5) liters

Step 3: Now, 'x' liters of water is added to the container.

Therefore, the total amount of water in the new mixture = 2 liters + (2x/5) liters + x liters

And the total amount of milk in the new mixture = 3 liters + (3x/5) liters

Step 4: We need to find the value of 'x' such that the new mixture contains water and milk in the ratio of 1:1.

Therefore, we can write the equation as:

2 + (2x/5) + x = 3 + (3x/5)

Simplifying the equation, we get:

2x/5 = 1/5

x = 1 liter

Step 5: Therefore, 1 liter of the mixture should be removed and replaced with 1 liter of water so that the new solution contains water and milk in the ratio of 1:1.

Conclusion:

To summarize, the milkman should remove 1 liter of the mixture and replace it with 1 liter of water so that the new solution contains water and milk in the ratio of 1:1.

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