In an examination, 35% of total students failed in Hindi, 45% failed in English and 20% in both. Find the percentage of those who passed in both the subjects.
Answer
Answer (as printed):
Explanation
Let A and B be the sets of students who failed in Hindi and English respectively. Then, n (A) = 35, n (B) = 45, n (A ∩ B) = 20. So, n (A ∪ B) = n (A) + n (B) – n (A ∩ B) = (35 + 45 – 20) = 60. ∴ Percentage failed in Hindi or English or both = 60%. Hence, percentage passed = (100 – 60)% = 40%.
Explanation as extracted from the printed page; notation may be imperfect.