In an examination, 80% of the students passed in English, 85% in Mathematics and 75% in both English and Mathematics. If 40 students failed in both the subjects, find the total number of students.
Answer
Answer (as printed):
Explanation
Let the total number of students be x. Let A and B represent the sets of students who passed in English and Mathematics respectively. Then, number of students passed in one or both the subjects = n (A ∪ B) = n (A) + n (B) – n (A ∩ B) = 80% of x + 85% of x – 75% of x 80 85 75 90 9 = x+ x− x = x= x. 100 100 100 100 10 9x x ∴ Students who failed in both the subjects = x − = . 10 10 x So, = 40 or x = 400. Hence, total number of students = 400. 10
Explanation as extracted from the printed page; notation may be imperfect.