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Out of 60 students 25 failed in paper (1), 24 in paper (2), 32 in paper (3), 9 in paper (1), alone 6 in paper (2), alone 5 in papers (2), and (3), and 3 in papers (1), and (2). Find how many passed in all the three papers?
- a)10
- b)60
- c)50
- d)None
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Out of 60 students 25 failed in paper (1), 24 in paper (2), 32 in pape...
Given information:
- Total number of students = 60
- Number of students failed in paper (1) = 25
- Number of students failed in paper (2) = 24
- Number of students failed in paper (3) = 32
- Number of students failed in paper (1) alone = 9
- Number of students failed in paper (2) alone = 6
- Number of students failed in papers (2) and (3) = 5
- Number of students failed in papers (1) and (2) = 3
To find: Number of students who passed in all three papers.
Solution:
First, we can find the number of students who failed in only two papers:
- Number of students failed in papers (2) and (3) = 5
- Number of students failed in papers (1) and (2) = 3
- Total = 5 + 3 = 8
Next, we can find the number of students who failed in only one paper:
- Number of students failed in paper (1) alone = 9
- Number of students failed in paper (2) alone = 6
- Number of students failed in paper (3) alone = (32 - 5) = 27
- Total = 9 + 6 + 27 = 42
Now, we can find the number of students who passed in at least two papers:
- Total number of students = 60
- Number of students who failed in at least one paper = 42
- Number of students who passed in at least two papers = 60 - 42 = 18
Finally, we can find the number of students who passed in all three papers:
- Number of students who passed in at least two papers = 18
- Number of students who failed in all three papers = 25 + 24 + 32 - 2*(5 + 3) = 43
- Number of students who passed in all three papers = Total - (Failed in at least one paper) - (Failed in all three papers)
= 60 - 42 - 43
= 10
Therefore, the number of students who passed in all three papers is 10, which is option (a).
- Total number of students = 60
- Number of students failed in paper (1) = 25
- Number of students failed in paper (2) = 24
- Number of students failed in paper (3) = 32
- Number of students failed in paper (1) alone = 9
- Number of students failed in paper (2) alone = 6
- Number of students failed in papers (2) and (3) = 5
- Number of students failed in papers (1) and (2) = 3
To find: Number of students who passed in all three papers.
Solution:
First, we can find the number of students who failed in only two papers:
- Number of students failed in papers (2) and (3) = 5
- Number of students failed in papers (1) and (2) = 3
- Total = 5 + 3 = 8
Next, we can find the number of students who failed in only one paper:
- Number of students failed in paper (1) alone = 9
- Number of students failed in paper (2) alone = 6
- Number of students failed in paper (3) alone = (32 - 5) = 27
- Total = 9 + 6 + 27 = 42
Now, we can find the number of students who passed in at least two papers:
- Total number of students = 60
- Number of students who failed in at least one paper = 42
- Number of students who passed in at least two papers = 60 - 42 = 18
Finally, we can find the number of students who passed in all three papers:
- Number of students who passed in at least two papers = 18
- Number of students who failed in all three papers = 25 + 24 + 32 - 2*(5 + 3) = 43
- Number of students who passed in all three papers = Total - (Failed in at least one paper) - (Failed in all three papers)
= 60 - 42 - 43
= 10
Therefore, the number of students who passed in all three papers is 10, which is option (a).
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Community Answer
Out of 60 students 25 failed in paper (1), 24 in paper (2), 32 in pape...
As per venn diagram
n(B)=n(B alone)+n(BnC)+n(AnC)+n(AnBnC)
24=6+5+3+n(AnBnC)
n(AnBnC)=24-14=10
n(B)=n(B alone)+n(BnC)+n(AnC)+n(AnBnC)
24=6+5+3+n(AnBnC)
n(AnBnC)=24-14=10
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Out of 60 students 25 failed in paper (1), 24 in paper (2), 32 in paper (3), 9 in paper (1), alone 6 in paper (2), alone 5 in papers (2), and (3), and 3 in papers (1), and (2). Find how many passed in all the three papers?a)10b)60c)50d)NoneCorrect answer is option 'A'. Can you explain this answer?
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