Question

. Out of 100 students; 15 passed in English, 12 in
Mathematics, 8 in Science, 6 in English and Mathematics,
7 in Mathematics and Science, 4 in English and Science
and 4 in all the three. Find how many students passed
(a) in English and Mathematics but not in Science
(b) in Mathematics and Science but not in English
(c) in Mathematics only
(d) in more than one subjects​

Answer 1

Answer:

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

To find : How many passed in following options ?

Solution :

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 is

b = 2

(ii) Number of students in Mathematics and Science but not in English is

d = 3

(iii) Number of students in Mathematics only is

e = 3

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

P= a + b + c + d

P= 4 + 3 + 2 + 0

P= 9