Question : In an examination, 45% of students passed in history and 60% of students passed in Hindi. If 8% of students failed in both subjects, then what percentage of students passed in both subjects?
Option 1: 15%
Option 2: 10%
Option 3: 13%
Option 4: 12%
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Correct Answer: 13%
Solution :
Students who passed in History = 45%
Students who failed in History [n(History)] = 100 – 45 = 55%
Students who passed in Hindi = 60%
Students who failed in Hindi [n(Hindi)] = 100 – 60= 40%
Students failed in both subjects [n(History∩Hindi)]= 8%
We know that,
n(History U Hindi) = n(History) + n(Hindi) – n(History∩Hindi)
⇒ n(History U Hindi) = 55 + 40 – 8
⇒ n(History U Hindi) = 87
$\therefore$ Students passed in both subjects = 100 – 87 = 13%
Hence, the correct answer is 13%.
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