Question

In a competitive exam 50 students passed in English, 60 students passed in Mathematics and 40 students passed in both the subjects. None of them failed in both the subjects. Find the number of students who passed at least in one of the subjects?

Answer 1

Let U be the set of students who appeared for the exam, 

E be the set of students who passed in English and 

M be the set of students who passed in Maths. 

∴ n(E) = 50, n(M) = 60, 

40 students passed in both the subjects 

∴ n(M ∩ E) = 40 

Since, none of the students failed in both subjects 

∴ Total students = n(E ∪M) 

= n(E) + n(M) – n(E ∩ M) 

= 50 + 60 – 40

= 70 

∴ The number of students who passed at least in one of the subjects is 70. 

Alternate Method: 

Let U be the set of students who appeared for the exam, 

E be the set of students who passed in English and M be the set of students who passed in Maths.

Since, none of the students failed in both subjects 

∴ Total student = n(E ∪M) 

= 10 + 40 + 20 

= 70

∴ The number of students who passed at least in one of the subjects is 70.