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A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is
Correct answer is '7'. Can you explain this answer?
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A container has 40 liters of milk. Then, 4 liters are removed from the...
Explanation:
Initial volume of milk:
- Initially, the container has 40 liters of milk.
Volume after each replacement:
- After each replacement of 4 liters of milk with 4 liters of water, the net volume of milk in the container decreases by 4 liters.
Number of replacements:
- After the first replacement, the volume of milk becomes 36 liters.
- After the second replacement, the volume of milk becomes 32 liters.
- After the third replacement, the volume of milk becomes 28 liters.
- After the fourth replacement, the volume of milk becomes 24 liters.
- After the fifth replacement, the volume of milk becomes 20 liters.
- After the sixth replacement, the volume of milk becomes 16 liters.
- After the seventh replacement, the volume of milk becomes 12 liters, which is less than the volume of water (28 liters).
Therefore, the smallest number of times the process needs to be repeated for the volume of milk to become less than that of water is 7.
Initial volume of milk:
- Initially, the container has 40 liters of milk.
Volume after each replacement:
- After each replacement of 4 liters of milk with 4 liters of water, the net volume of milk in the container decreases by 4 liters.
Number of replacements:
- After the first replacement, the volume of milk becomes 36 liters.
- After the second replacement, the volume of milk becomes 32 liters.
- After the third replacement, the volume of milk becomes 28 liters.
- After the fourth replacement, the volume of milk becomes 24 liters.
- After the fifth replacement, the volume of milk becomes 20 liters.
- After the sixth replacement, the volume of milk becomes 16 liters.
- After the seventh replacement, the volume of milk becomes 12 liters, which is less than the volume of water (28 liters).
Therefore, the smallest number of times the process needs to be repeated for the volume of milk to become less than that of water is 7.
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Community Answer
A container has 40 liters of milk. Then, 4 liters are removed from the...
Every time 10% of the mixture is replace with a pure adulterant (here water), the concentration of the mixture becomes 90% of the initial concentration.
Similarly when a proportion p of a mixture is replaced with pure adulterant, the concentration of the mixture becomes (1 - p) times the previous concentration. (0 ≤ p ≤ 1)
Similarly when a proportion p of a mixture is replaced with pure adulterant, the concentration of the mixture becomes (1 - p) times the previous concentration. (0 ≤ p ≤ 1)
Here p = 4/40 = 0.1
Initially there was pure milk, so the strength of the mixture is 100% or 1 (in terms of proportion)
After repeating the process n times the concentration of Milk in the mixture will be 1×0.9n
For the volume of milk to be less than the volume of water, p should be less than 0.5
So we are looking for the smallest n, such that 1 × 0.9n < 0.5
This happens when n = 7
Initially there was pure milk, so the strength of the mixture is 100% or 1 (in terms of proportion)
After repeating the process n times the concentration of Milk in the mixture will be 1×0.9n
For the volume of milk to be less than the volume of water, p should be less than 0.5
So we are looking for the smallest n, such that 1 × 0.9n < 0.5
This happens when n = 7
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A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, isCorrect answer is '7'. Can you explain this answer?
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A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, isCorrect answer is '7'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, isCorrect answer is '7'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, isCorrect answer is '7'. Can you explain this answer?.
A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, isCorrect answer is '7'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, isCorrect answer is '7'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, isCorrect answer is '7'. Can you explain this answer?.
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