Question

In an examination 50% of the students passed in Mathematics and 70% of students passed in Science while 10% students failed in both subjects. 300 students passed in both the subjects. Find the total number of students who appeared in the examination, if they took examination in only two subjects

Answer 1

Let M and S represent the student failed in Mathematics and Science.

Given: Number of students passed in Mathematics is 50%

∴ Number of students failed in Mathematics

= 100 – 50%

= 50%

n(M) = 50%

Number of students passed in Science is 70%

∴ Number of students failed in Science

= 100 – 70%

= 30%

n(S) = 30%

Number of students failed in both the subjects is 10%

n(M ∩ S) = 10%

n(M ∪ S) = n(M) + n(S) – n(M ∩ S)

= 50 + 30 – 10

= 80 – 10

= 70

Given: 70% of the students failed in atleast any one of the subject

∴ 30% of the students passed in atleast any one of the subjects.

30 students passed mean, the total number of students is 100.

∴ 300 students passed means, the total number of students = `(100 xx 300)/30`

Total number of students appeared in the examination = 1000