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In an examination, 34% of the students failed in mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then find the percentage of students who passed in both the subjects.
- a)40%
- b)41%
- c)43%
- d)44%
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In an examination, 34% of the students failed in mathematics and 42% f...
Failed in mathematics, n(A) = 34 Failed in English, n(B) = 42
n(AUB) = n(A) + n (B) – n (A∩ B )
= 34 + 42- 20 = 56 Failed in either or both subjects are 56
Percentage passed = (100-56)%=44%
n(AUB) = n(A) + n (B) – n (A∩ B )
= 34 + 42- 20 = 56 Failed in either or both subjects are 56
Percentage passed = (100-56)%=44%
Most Upvoted Answer
In an examination, 34% of the students failed in mathematics and 42% f...
Given Information:
- 34% of the students failed in mathematics.
- 42% of the students failed in English.
- 20% of the students failed in both subjects.
To Find:
The percentage of students who passed in both subjects.
Approach:
To find the percentage of students who passed in both subjects, we need to subtract the percentage of students who failed in both subjects from 100%.
Solution:
Let's assume the total number of students is 100.
- Number of students failed in mathematics = 34% of 100 = 34 students
- Number of students failed in English = 42% of 100 = 42 students
- Number of students failed in both subjects = 20% of 100 = 20 students
Step 1: Calculate the number of students who failed in at least one subject.
- Number of students who failed in at least one subject = Number of students failed in mathematics + Number of students failed in English - Number of students failed in both subjects
= 34 + 42 - 20
= 56 students
Step 2: Calculate the number of students who passed in both subjects.
- Number of students who passed in both subjects = Total number of students - Number of students who failed in at least one subject
= 100 - 56
= 44 students
Step 3: Calculate the percentage of students who passed in both subjects.
- Percentage of students who passed in both subjects = (Number of students who passed in both subjects / Total number of students) x 100%
= (44 / 100) x 100%
= 44%
Therefore, the percentage of students who passed in both mathematics and English is 44%.
Answer:
The correct answer is option D) 44%.
- 34% of the students failed in mathematics.
- 42% of the students failed in English.
- 20% of the students failed in both subjects.
To Find:
The percentage of students who passed in both subjects.
Approach:
To find the percentage of students who passed in both subjects, we need to subtract the percentage of students who failed in both subjects from 100%.
Solution:
Let's assume the total number of students is 100.
- Number of students failed in mathematics = 34% of 100 = 34 students
- Number of students failed in English = 42% of 100 = 42 students
- Number of students failed in both subjects = 20% of 100 = 20 students
Step 1: Calculate the number of students who failed in at least one subject.
- Number of students who failed in at least one subject = Number of students failed in mathematics + Number of students failed in English - Number of students failed in both subjects
= 34 + 42 - 20
= 56 students
Step 2: Calculate the number of students who passed in both subjects.
- Number of students who passed in both subjects = Total number of students - Number of students who failed in at least one subject
= 100 - 56
= 44 students
Step 3: Calculate the percentage of students who passed in both subjects.
- Percentage of students who passed in both subjects = (Number of students who passed in both subjects / Total number of students) x 100%
= (44 / 100) x 100%
= 44%
Therefore, the percentage of students who passed in both mathematics and English is 44%.
Answer:
The correct answer is option D) 44%.
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