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In an examination, 35% of total students failed in Hindi, 45% failed in English and 20% failed in both. Find the percentage of those students who passed in both the subjects?
- a)45%
- b)35%
- c)20%
- d)40%
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In an examination, 35% of total students failed in Hindi, 45% failed i...
From given data
No of students failed in Hindi n(H) = 35%
No of students failed in English n(E) = 45%
No of students failed in both n(H ∩ E) = 20%
⇒ total number of students who failed n(H ⋃ E) = n(H) + n(E) – n(H ∩ E)
⇒ n(H ⋃ E) = 35 + 45 - 20
⇒ n(H ⋃ E) = 60
No of students who passed = 100 - (total no of students who failed) = 100 – 60 = 40%
No of students failed in Hindi n(H) = 35%
No of students failed in English n(E) = 45%
No of students failed in both n(H ∩ E) = 20%
⇒ total number of students who failed n(H ⋃ E) = n(H) + n(E) – n(H ∩ E)
⇒ n(H ⋃ E) = 35 + 45 - 20
⇒ n(H ⋃ E) = 60
No of students who passed = 100 - (total no of students who failed) = 100 – 60 = 40%
Most Upvoted Answer
In an examination, 35% of total students failed in Hindi, 45% failed i...
Understanding the Problem
To find the percentage of students who passed both subjects, we can use the principle of inclusion-exclusion.
Given Data
- Percentage of students who failed in Hindi = 35%
- Percentage of students who failed in English = 45%
- Percentage of students who failed in both subjects = 20%
Calculating Overall Failures
Using the inclusion-exclusion principle, we can calculate the percentage of students who failed at least one subject:
- Percentage of students failing at least one subject = (Percentage failing Hindi) + (Percentage failing English) - (Percentage failing both)
- Plugging in the values:
- Percentage failing at least one subject = 35% + 45% - 20%
- Percentage failing at least one subject = 60%
Calculating Pass Percentage
Now, to find the percentage of students who passed both subjects:
- Percentage of students who passed both subjects = 100% - Percentage failing at least one subject
- Thus:
- Percentage of students who passed both subjects = 100% - 60%
- Percentage of students who passed both subjects = 40%
Conclusion
The percentage of students who passed in both subjects is:
- 40%
Thus, the correct answer is option 'D'.
To find the percentage of students who passed both subjects, we can use the principle of inclusion-exclusion.
Given Data
- Percentage of students who failed in Hindi = 35%
- Percentage of students who failed in English = 45%
- Percentage of students who failed in both subjects = 20%
Calculating Overall Failures
Using the inclusion-exclusion principle, we can calculate the percentage of students who failed at least one subject:
- Percentage of students failing at least one subject = (Percentage failing Hindi) + (Percentage failing English) - (Percentage failing both)
- Plugging in the values:
- Percentage failing at least one subject = 35% + 45% - 20%
- Percentage failing at least one subject = 60%
Calculating Pass Percentage
Now, to find the percentage of students who passed both subjects:
- Percentage of students who passed both subjects = 100% - Percentage failing at least one subject
- Thus:
- Percentage of students who passed both subjects = 100% - 60%
- Percentage of students who passed both subjects = 40%
Conclusion
The percentage of students who passed in both subjects is:
- 40%
Thus, the correct answer is option 'D'.
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In an examination, 35% of total students failed in Hindi, 45% failed in English and 20% failed in both. Find the percentage of those students who passed in both the subjects?a)45%b)35%c)20%d)40%Correct answer is option 'D'. Can you explain this answer?
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