Question

In an examination out of 100 students, 75 passed in english, 60 passed in mathematics and 45 passed in both english and mathematics. What is the number of students passed in exactly one of the two subjects ?
(a) 45 (b) 60 (c) 75 (d) 90
answer is (a) 45 HOW? (please write the steps because i know the answer just wanted the steps)

Answer 1

Correct option: (d) 90.

Step-by-step explanation:

Total number of students, N = 100.

Number of students who passed in English, n (E) = 75.

Number of students who passed in Mathematics, n (M) = 60.

Number of students who passed in both, n (E ∩ M) = 45.

Compute the number of students passed in exactly one of the two subjects as follows:

n (E ∪ M) = n (E) + n (M) - n (E ∩ M)

               = 75 + 60 - 45

               = 90

Thus, the number of students passed in exactly one of the two subjects is 90.

Answer 2

Cardinal number of E is equals to 100.

i.e - n(E) = 100

The total number of students passed only in English = 75 - 45 = 30

total number of student passed only in maths

= 60 - 45 = 15

So,

number of student passed in exactly one of the two subject is 30 + 15 = 45