In a school, every student takes Hindi or English or both. 50.8% take Hindi…
2023
In a school, every student takes Hindi or English or both. 50.8% take Hindi and 64.2% take English. If the total number of students is 500, how many students take both Hindi and English?
Answer: C. 75 — ConceptFor two sets A and B, inclusion–exclusion states that the size of their intersection equals the sum of their individual sizes minus the size of their…
- A.
60
- B.
65
- C.
75
- D.
More than one of the above
- E.
None of the above
Attempted by 10 students.
Show answer & explanation
Correct answer: C
Concept
For two sets A and B, inclusion–exclusion states that the size of their intersection equals the sum of their individual sizes minus the size of their union.
If every member belongs to at least one of the two sets, the union is the entire population, or 100%.
Application
Let H be the set of students taking Hindi and E the set taking English. Since every student takes at least one language, P(H ∪ E) = 100%.
Apply inclusion–exclusion: P(H ∩ E) = 50.8% + 64.2% − 100% = 15%.
Convert the overlap percentage to a count: (15/100) × 500 = 75 students.
Cross-check
Hindi only is 50.8% − 15% = 35.8%, and English only is 64.2% − 15% = 49.2%. Then 35.8% + 15% + 49.2% = 100%, so the partition accounts for every student.
Therefore, 75 students take both Hindi and English.