In an examination, 65% students passed in Mathematics and 60% students in English, 40% passed in both these subjects. If 90 students failed in Mathematics and English both, then what is the total number of students?

Question: In an examination, 65% students passed in Mathematics and 60% students in English, 40% passed in both these subjects. If 90 students failed in Mathematics and English both, then what is the total number of students?

Solution:
Given that,
P(M) = 65%
P(E) = 60%
P(M ∩ E) = 40%

We know,
P(M U E) = P(M) + P(E) - P(M ∩ E)
= 65% + 60% - 40% = 85%
∴ P(M U E) = 85%
∴ passed students = 85%
∴ Failed students = 100% - 85% = 15%

Now,
We are given that 90 students failed in both subjects, which represents 15% of the total students. Let N be the total number of students.
⇒ 15% of N = 90
⇒ (15/100)N = 90
⇒ N = (90 × 100)/15
∴ N = 600

∴ The total number of students is 600.