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A vessel is filled to its capacity with pure milk 32 L are withdrawn from the vessel and replace with an equal amount of water 32 L of the mixture is again withdrawn and then replaced with an equal amount of water. After these changes the vessel contain 51.2 L of milk less than it did initially what is the minimum number of such additional replacement required, so that the vessel contain less than 10% of milk?
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A vessel is filled to its capacity with pure milk 32 L are withdrawn f...
Initial Setup
The vessel starts with 32 L of pure milk. When 32 L of milk is withdrawn and replaced with 32 L of water, the concentration of milk in the mixture changes.
First Replacement
- **Initial Volume of Milk**: 32 L
- **Milk Withdrawn**: 32 L
- **Water Added**: 32 L
After the first replacement, the vessel is now filled with a total of 32 L of a milk-water mixture, which initially contains no milk.
Second Replacement
- **New Mixture Volume**: 32 L
- **Milk Content**: (32 L - 32 L) = 0 L
After withdrawing 32 L of the mixture again, you are effectively removing some milk.
Final Milk Calculation
According to the problem, after two replacements, the vessel contains 51.2 L less milk than initially. This indicates that we have effectively diluted the milk content each time we replaced it with water.
Calculating Further Replacements
The concentration of milk after each replacement can be modeled as:
- **Remaining Milk**: \( V_m = V_0 \left(1 - \frac{n}{V}\right)^n \)
Where:
- \( V_0 \) = Initial volume of milk (32 L)
- \( n \) = Volume of milk withdrawn (32 L)
- \( V \) = Total volume (32 L)
To find the minimum number of replacements (\( n \)) required for milk concentration to be less than 10%:
- Set up the inequality:
\[ V_m < 0.1="" \times="" 32="" />
Solving this inequality, you will find that a minimum of **four replacements** is needed to achieve a milk concentration of less than 10%.
Conclusion
By conducting replacements strategically, the concentration of milk can be reduced significantly, achieving the desired threshold.
The vessel starts with 32 L of pure milk. When 32 L of milk is withdrawn and replaced with 32 L of water, the concentration of milk in the mixture changes.
First Replacement
- **Initial Volume of Milk**: 32 L
- **Milk Withdrawn**: 32 L
- **Water Added**: 32 L
After the first replacement, the vessel is now filled with a total of 32 L of a milk-water mixture, which initially contains no milk.
Second Replacement
- **New Mixture Volume**: 32 L
- **Milk Content**: (32 L - 32 L) = 0 L
After withdrawing 32 L of the mixture again, you are effectively removing some milk.
Final Milk Calculation
According to the problem, after two replacements, the vessel contains 51.2 L less milk than initially. This indicates that we have effectively diluted the milk content each time we replaced it with water.
Calculating Further Replacements
The concentration of milk after each replacement can be modeled as:
- **Remaining Milk**: \( V_m = V_0 \left(1 - \frac{n}{V}\right)^n \)
Where:
- \( V_0 \) = Initial volume of milk (32 L)
- \( n \) = Volume of milk withdrawn (32 L)
- \( V \) = Total volume (32 L)
To find the minimum number of replacements (\( n \)) required for milk concentration to be less than 10%:
- Set up the inequality:
\[ V_m < 0.1="" \times="" 32="" />
Solving this inequality, you will find that a minimum of **four replacements** is needed to achieve a milk concentration of less than 10%.
Conclusion
By conducting replacements strategically, the concentration of milk can be reduced significantly, achieving the desired threshold.
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A vessel is filled to its capacity with pure milk 32 L are withdrawn from the vessel and replace with an equal amount of water 32 L of the mixture is again withdrawn and then replaced with an equal amount of water. After these changes the vessel contain 51.2 L of milk less than it did initially what is the minimum number of such additional replacement required, so that the vessel contain less than 10% of milk?
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A vessel is filled to its capacity with pure milk 32 L are withdrawn from the vessel and replace with an equal amount of water 32 L of the mixture is again withdrawn and then replaced with an equal amount of water. After these changes the vessel contain 51.2 L of milk less than it did initially what is the minimum number of such additional replacement required, so that the vessel contain less than 10% of milk? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A vessel is filled to its capacity with pure milk 32 L are withdrawn from the vessel and replace with an equal amount of water 32 L of the mixture is again withdrawn and then replaced with an equal amount of water. After these changes the vessel contain 51.2 L of milk less than it did initially what is the minimum number of such additional replacement required, so that the vessel contain less than 10% of milk? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vessel is filled to its capacity with pure milk 32 L are withdrawn from the vessel and replace with an equal amount of water 32 L of the mixture is again withdrawn and then replaced with an equal amount of water. After these changes the vessel contain 51.2 L of milk less than it did initially what is the minimum number of such additional replacement required, so that the vessel contain less than 10% of milk?.
A vessel is filled to its capacity with pure milk 32 L are withdrawn from the vessel and replace with an equal amount of water 32 L of the mixture is again withdrawn and then replaced with an equal amount of water. After these changes the vessel contain 51.2 L of milk less than it did initially what is the minimum number of such additional replacement required, so that the vessel contain less than 10% of milk? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A vessel is filled to its capacity with pure milk 32 L are withdrawn from the vessel and replace with an equal amount of water 32 L of the mixture is again withdrawn and then replaced with an equal amount of water. After these changes the vessel contain 51.2 L of milk less than it did initially what is the minimum number of such additional replacement required, so that the vessel contain less than 10% of milk? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vessel is filled to its capacity with pure milk 32 L are withdrawn from the vessel and replace with an equal amount of water 32 L of the mixture is again withdrawn and then replaced with an equal amount of water. After these changes the vessel contain 51.2 L of milk less than it did initially what is the minimum number of such additional replacement required, so that the vessel contain less than 10% of milk?.
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A vessel is filled to its capacity with pure milk 32 L are withdrawn from the vessel and replace with an equal amount of water 32 L of the mixture is again withdrawn and then replaced with an equal amount of water. After these changes the vessel contain 51.2 L of milk less than it did initially what is the minimum number of such additional replacement required, so that the vessel contain less than 10% of milk?, a detailed solution for A vessel is filled to its capacity with pure milk 32 L are withdrawn from the vessel and replace with an equal amount of water 32 L of the mixture is again withdrawn and then replaced with an equal amount of water. After these changes the vessel contain 51.2 L of milk less than it did initially what is the minimum number of such additional replacement required, so that the vessel contain less than 10% of milk? has been provided alongside types of A vessel is filled to its capacity with pure milk 32 L are withdrawn from the vessel and replace with an equal amount of water 32 L of the mixture is again withdrawn and then replaced with an equal amount of water. After these changes the vessel contain 51.2 L of milk less than it did initially what is the minimum number of such additional replacement required, so that the vessel contain less than 10% of milk? theory, EduRev gives you an
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