Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed (iii) in Mathematics only (iv) in more than one subject only.

Solution:

As per the question,

100 = Total number of students

15 = Number of students who passed in English

12 = Number of students who passed in Mathematics

8 = Number of students who passed in Science

6 = Number of students who passed in English and Mathematics

7 = Number of students who passed in Mathematics and Science

4 = Number of students who passed in English and Science

4 = Number of students who passed in all three

U = Let the total number of students

E = Let the number of students passed in English

M = Let the number of students passed in Mathematics

S = Let the number of students passed in Science

As a result, from the above equations, we have,

(i) e = 3 = Number of students in Mathematics only

(ii) a + b + c + d = 4 + 3 + 2 + 0 = 9 = Number of students in more than one subject only