In an examination, 34% of the students failed in mathematics and 42% failed in English. If 20% of the students failed in both subjects, then find the percentage of students who passed in both subjects.
5Q:
In an examination, 34% of the students failed in mathematics and 42% failed in English. If 20% of the students failed in both subjects, then find the percentage of students who passed in both subjects.
- 140%false
- 241%false
- 343%false
- 444%true
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Answer : 4. "44%"
Explanation :
To find the percentage of students who failed in at least one subject (A or B or both), we can use the principle of inclusion-exclusion:
Percentage of students who failed in at least one subject (A or B or both) = Percentage of students who failed in M + Percentage of students who failed in E - Percentage of students who failed in both subjects
= M + E - B
= 34% + 42% - 20% = 76% - 20% = 56%
So, 56% of the students failed in at least one subject.
Now, to find the percentage of students who passed in both subjects, we subtract the percentage of students who failed in at least one subject from 100%:
Percentage of students who passed in both subjects = 100% - Percentage of students who failed in at least one subject = 100% - 56% = 44%
Therefore, the percentage of students who passed in both subjects is 44%.