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.
A
350
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B
400
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C
450
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D
500
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Solution
The correct option is B 400 Let the total number of student is x Number of student passed in both subject is n(A∪B)=n(A)+n(B)−(A∩B) Here, n(A)=80% of x n(B)=85% of x n(c)=75% of x ∴n(A∪B)=80100x+85100x−75100x ⇒90x100⇒9x10 Failed in both subjects ⇒x−9x10⇒x10 ∴x10=40 ⇒x=400