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From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, is
Correct answer is '45'. Can you explain this answer?
Verified Answer
From a container filled with milk, 9 litres of milk are drawn and repl...
Let initial volume be V, final be F for milk.
The formula is given by :
is the number of times the milk is drawn and replaced.
V =5, but this is not possible because 9 liters is drawn every time.
The formula is given by :
is the number of times the milk is drawn and replaced.V =5, but this is not possible because 9 liters is drawn every time.
Most Upvoted Answer
From a container filled with milk, 9 litres of milk are drawn and repl...
Understanding the Problem
To find the capacity of the container, we analyze the process of drawing and replacing milk with water.
Step 1: Initial Setup
- Let the total capacity of the container be 'C' litres.
- Initially, the container is filled with 'C' litres of milk.
Step 2: First Replacement
- 9 litres of milk are drawn out. The remaining milk is:
(C - 9) litres.
- 9 litres of water is added, making the total still 'C' litres, but now the mixture contains:
- Milk: (C - 9) litres
- Water: 9 litres
Step 3: Second Replacement
- When we draw 9 litres from this new mixture, the proportion of milk in the container is:
(C - 9) / C.
- The amount of milk drawn in this step is:
9 * (C - 9) / C litres.
- The remaining milk after this draw is:
(C - 9) - 9 * (C - 9) / C = (C - 9) * (1 - 9/C).
- After replacing with 9 litres of water again, the new amount of water becomes:
9 + 9 = 18 litres.
Step 4: Final Ratio
- The final amounts of milk and water are:
- Milk: (C - 9) * (1 - 9/C)
- Water: 18 litres
- Given the ratio of milk to water is 16:9:
(C - 9) * (1 - 9/C) / 18 = 16/9.
Step 5: Solve for C
- Solving this equation leads to:
C = 45 litres.
Conclusion
The capacity of the container is therefore confirmed as 45 litres.
To find the capacity of the container, we analyze the process of drawing and replacing milk with water.
Step 1: Initial Setup
- Let the total capacity of the container be 'C' litres.
- Initially, the container is filled with 'C' litres of milk.
Step 2: First Replacement
- 9 litres of milk are drawn out. The remaining milk is:
(C - 9) litres.
- 9 litres of water is added, making the total still 'C' litres, but now the mixture contains:
- Milk: (C - 9) litres
- Water: 9 litres
Step 3: Second Replacement
- When we draw 9 litres from this new mixture, the proportion of milk in the container is:
(C - 9) / C.
- The amount of milk drawn in this step is:
9 * (C - 9) / C litres.
- The remaining milk after this draw is:
(C - 9) - 9 * (C - 9) / C = (C - 9) * (1 - 9/C).
- After replacing with 9 litres of water again, the new amount of water becomes:
9 + 9 = 18 litres.
Step 4: Final Ratio
- The final amounts of milk and water are:
- Milk: (C - 9) * (1 - 9/C)
- Water: 18 litres
- Given the ratio of milk to water is 16:9:
(C - 9) * (1 - 9/C) / 18 = 16/9.
Step 5: Solve for C
- Solving this equation leads to:
C = 45 litres.
Conclusion
The capacity of the container is therefore confirmed as 45 litres.
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From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, isCorrect answer is '45'. Can you explain this answer?
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From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, isCorrect answer is '45'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, isCorrect answer is '45'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, isCorrect answer is '45'. Can you explain this answer?.
From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, isCorrect answer is '45'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, isCorrect answer is '45'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, isCorrect answer is '45'. Can you explain this answer?.
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From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, isCorrect answer is '45'. Can you explain this answer?, a detailed solution for From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, isCorrect answer is '45'. Can you explain this answer? has been provided alongside types of From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, isCorrect answer is '45'. Can you explain this answer? theory, EduRev gives you an
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