Question

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 1

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 

=[(80/100)x+(85/100)x-(75/100)x]=(90/100)x=(9/10)x 

Students who failed in both the subjects = [x-(9x/10)]=x/10. 

So, x/10=40 of x=400 . 

Hence ,total number of students = 400.