Question

In an examination, out of 260 students, 190 students passed in English, 75 in science and 60 in maths. For every person wgo failed in English, there were 2 persons who failed in science and 3 in maths alone.The number of students who passed in 2 subjects are 5 more than the students who passed in all three. Also, those who passed in English with only one other subject were equal in number to those who passed all three subjects. Find the number of students who failed in all threethreeo​

Answer 1

Answer:

Let A be the set of students passed in English and B be the set of students who passed in maths.

Since 25% failed in both, percentage of students who passed at least one subject is (100–25)% = 75%. ie n(AUB) =75 if we take 100 as the total number of students.

But n(AUB) = n(A)+n(B) - n(AnB)

=> n(AnB) = 75+60–75 = 60

So percentage of students who passed the exam is 60%

So 60% of the students = 240

100% of the students = 240/60 × 100 = 400

So total number of candidates= 400