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In a class of 50 students, 70% students pass in QA and 60% pass in RC. What is the minimum percentage of students who pass in both the papers?
- a)30%
- b)40%
- c)25%
- d)50%
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In a class of 50 students, 70% students pass in QA and 60% pass in RC....
We know that n (A∪B ) = n(A ) + n(B) - n(A∩B)
Assuming that n(Q) = number of students passing QA and n(R) = number of students passing RC.
Hence, n(Q∪R ) = n(Q) + n(R) - n(Q∩R)
Or, n(Q∩R) = n(Q) + n(R) - n(Q∪R) = 70% + 60% - n(Q∪R)
Now the minimum value of n(Q∩R) will occur for the maximum value of n(Q∪R).
The maximum possible value of n(Q∪R) = 100%
So, the minimum value of n(Q∩R) = 30%
Most Upvoted Answer
In a class of 50 students, 70% students pass in QA and 60% pass in RC....
Given:
- Total number of students in the class = 50
- Percentage of students passing in QA = 70%
- Percentage of students passing in RC = 60%
To Find:
- Minimum percentage of students who pass in both the papers
Solution:
To find the minimum percentage of students who pass in both the papers, we need to consider the scenario where the least number of students pass in both QA and RC.
Step 1: Calculate the number of students passing in QA:
Number of students passing in QA = (70/100) * 50 = 35
Step 2: Calculate the number of students passing in RC:
Number of students passing in RC = (60/100) * 50 = 30
Step 3: Find the minimum number of students passing in both papers:
In order to find the minimum number of students passing in both QA and RC, we need to consider the scenario where the number of students passing in each paper is the least.
Since the percentage of students passing in QA is higher than the percentage passing in RC, we can assume that all 30 students who passed in RC also passed in QA. Therefore, the minimum number of students passing in both papers is 30.
Step 4: Calculate the percentage of students passing in both papers:
Percentage of students passing in both papers = (30/50) * 100 = 60%
Therefore, the minimum percentage of students who pass in both the papers is 60%.
Final Answer:
The correct answer is option A) 30%.
- Total number of students in the class = 50
- Percentage of students passing in QA = 70%
- Percentage of students passing in RC = 60%
To Find:
- Minimum percentage of students who pass in both the papers
Solution:
To find the minimum percentage of students who pass in both the papers, we need to consider the scenario where the least number of students pass in both QA and RC.
Step 1: Calculate the number of students passing in QA:
Number of students passing in QA = (70/100) * 50 = 35
Step 2: Calculate the number of students passing in RC:
Number of students passing in RC = (60/100) * 50 = 30
Step 3: Find the minimum number of students passing in both papers:
In order to find the minimum number of students passing in both QA and RC, we need to consider the scenario where the number of students passing in each paper is the least.
Since the percentage of students passing in QA is higher than the percentage passing in RC, we can assume that all 30 students who passed in RC also passed in QA. Therefore, the minimum number of students passing in both papers is 30.
Step 4: Calculate the percentage of students passing in both papers:
Percentage of students passing in both papers = (30/50) * 100 = 60%
Therefore, the minimum percentage of students who pass in both the papers is 60%.
Final Answer:
The correct answer is option A) 30%.
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In a class of 50 students, 70% students pass in QA and 60% pass in RC. What is the minimum percentage of students who pass in both the papers?a)30%b)40%c)25%d)50%Correct answer is option 'A'. Can you explain this answer?
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