Discussion
In an exam, 49% students failed in English and 36% students failed in Hindi, while 15% failed in both. If the total number of students who passed the exam in both subjects was 675, what was the total number of students who appeared in the exam?
Answer: C
Let F(E) be the percentage of students who failed in English and F(H) be the percentage who failed in Hindi.
Given: n(F(E)) = 49%, n(F(H)) = 36%, n(F(E) ∩ F(H)) = 15%.
The percentage of students who failed in at least one subject is n(F(E) ∪ F(H)).
n(F(E) ∪ F(H)) = n(F(E)) + n(F(H)) - n(F(E) ∩ F(H)) = 49 + 36 - 15 = 70%.
The students who passed in both subjects are those who did not fail in any subject. This is the complement of failing in at least one subject.
Percentage Passed in both = 100% - n(F(E) ∪ F(H)) = 100% - 70% = 30%.
We are given that this number is 675. Let T be the total number of students.
30% of T = 675
0.30 × T = 675
T = 675 / 0.3 = 2250.
The total number of students was 2250.
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