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Using set theory let A contain the students who failed mathematics (50) and B contain the students that failed English (30). Now set A and B intersect so they share the same students (5). Therefore the students who passed both subjects is the complement of the union of the sets. ~(AUB)=~(A+B-AintersectB)=100-(50+30-5)=25 students.

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Q: N class of 100 students 50 students passed in Mathematics and 70 passed in English 5 students failed in both Mathematics and English How many students passed in both the subjects?
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In an examination 70 percent of the candidates passed in English 65 percent passed in Mathematics and 27 percent failed in both subjects What is the pass percentage?

Answer:100% (all students who took the test).Since 27% failed in both, then 73% are remained to be discussed.Since 70% passed in English, 65% passed in Math and 27% failed in both,Then, failed in English = (100% - 70%) = 30%.Failed only in English = 30% - 27% = 3%.Failed in Math = (100% - 65%) = 35%.Failed only in Math = 35% - 27% = 8%.So total % of students failed = failed in both subjects + failed in English only + failed in Math only = 27% + 3% + 8%= 38%.So passed in both subjects = 100% - 38% = 62%.Answer: In that exam 62% passed in both subjects.


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