Q. 244.5( 20 Votes )

Out of 100 studen

Answer :

Given:


Total number of students = 100


Number of students passed in English = 15


Number of students passed in Mathematics = 12


Number of students passed in Science = 8


Number of students passed in English and Mathematics = 6


Number of students passed in Mathematics and Science = 7


Number of students passed in English and Science = 4


Number of students passed in all three = 4


Let U be the total number of students, E, M and S be the number of students passed in English, Mathematics and Science respectively



n(M S E) = a = 4


n(M S) = a + d = 7


4 + d = 7


d = 3


n(M E) = a + b = 6


4 + b = 6


b = 2


n(S E) = a + c = 4


4 + c = 4


c = 0


n(M) = e + d + a + b = 12


e + 4 + 3 + 2 = 12


e + 9 = 12


e = 3


n(E) = g + c + a + b = 15


g + 0 + 4 + 2 = 15


g + 6 = 15


g = 9


n(S) = f + c + a + d = 8


f + 0 + 4 + 3 = 8


f + 7 = 8


f = 1


(i) Number of students passed in English and Mathematics but not in Science = b = 2


(ii) Number of students in Mathematics and Science but not in English = d = 3


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


(iv) Number of students in more than one subject only


= a + b + c + d


= 4 + 3 + 2 + 0


= 9


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