Mr. GUPTA runs a coaching class for school students. There are a total of 450 students enrolled in the coaching class. If 320 students are enrolled in the subject Maths and 270 are enrolled in Chemistry then, how many of the students are enrolled in both the subjects?
Answers
140 students are enrolled in both subjects.
Given: Total number of students enrolled in coaching class = 450
Number of students enrolled in Maths = 320
Number of students enrolled in Chemistry = 270
To find: Number of students enrolled in both the subjects
Let: M be the set of students enrolled in Maths and C be the set of students enrolled in Chemistry
Solution: According to the given problem,
Number of students enrolled in the coaching class = 450
i.e., 450 include students who are either enrolled in one of the subjects or in both subjects.
.: n(M∪C) = 450
Number of students enrolled in Maths = 320
.: n(M) = 320
Number of students enrolled in Chemistry = 270
.: n(C) = 270
Using the formula of finite sets
.: n(M∪C) = n(M) + n(C) - n(M∩C)
To find the number of students enrolled in both the subjects, we need to find n(M∩C)
.: n(M∩C) = n(M) + n(C) - n(M∪C)
= 320 + 270 - 450
= 590 - 450 = 140
Hence, 140 students are enrolled in both the subjects.