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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.


Options:
A .  350
B .  375
C .  400
D .  450
E .  ` root8(2)`
Answer: Option C

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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