Question

In a class of 100 students, 55 students have passed in maths and 67 students have passed in physics. Then the number of students who have passed in physics only is

Answer 1

Let M denote the sets of students who have passed in Mathematics...
And P denote the sets of students who have passed in Physics...

Thus from the question we get :-
n(M∪P) = 100
n(M) = 55
n(P) = 67

Thus n(M∩P) = n(M) + n(P) - n(M∪P)
         n(M∩P) = 55 + 67 - 100
         n(M∩P) = 22

Therefore the no. of who passed in physics only is given by :
                  = n(P) - n(M∩P)
                  = 67 - 22
                  = 45

Answer 2

Total no. of students in class = 100.... No. of students who passed in maths= 55............ And............ No. of students who passed in physics= 67............. No. of students who passed in both, i.e. maths as well as physics= 67+55=122........ No of students passed only in physics= 67-(122-100)....... = 67-22= 45 students.....