in an examination 80 of the students passed in english 85..., Percentage, General Mathematics

Question: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, the total number of students is :

A `200` 
B `400` 
C `600` 
D `800`

/114

+ AnswerB

+ ExplanationLet the total number of students be x.

Number passed in one or both is given by :

`n (AuuB) = n (A) + n (B) - n (AnnB)`

`= 80% of x + 85% of x - 75% of x.`

`= (80/(100) x + 85/(100) x - 75/(100) x)`

`= 90/(100) x`

`= (9x)/10.`

Failed in both

`= (x - (9x)/100)`

`= x/10.`

`:. x/10 = 40`

`or x = 400`.

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