In an examination, 80% of the students passed in English, 85% in Mathematics and 75 % in both English and
Mathematics. If 40 students failed in both the subjects , find the total number of students.
Let the total number of students be `x`
Let A and B represent the sets of students who passed in English and Mathematics respectively.
Then, number of students passed in one or both the subjects
= n (A`uu` B) = n(A) + n(B) - n(A`nn` B) = 80% of `x` + 85% of `x` - 75% of `x`
=`(80/100 x + 85/100 x - 75/100 x)` = `90/100 x = 9/10 x`
Students who failed in both the subjects = `(x - (9x)/(10)) = x/10`
So, `x/10`= 40 of x = 400. Hence total number of students = 400.
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