Question

in an exam 80% of the students passed in Eng, 85% in Math and 75% in both. if 40 students failed in both subjects, the total number of students is?

Answer 1

let n(A) = no. of students pass in english
    n(B) = no. of students pass in math
    n(AunionB) = no. of students pass in either math or english
    n(AintersectionB) = no.of students pass in both math and english
let x are no. of students
n(AunionB) = n(A) + n(B) - n(AintersectionB)
                 = 80x/100 + 85x/100 - 75x/100
                 = 90x/100
no. of students fail in both either math or english = x - n(AunionB)
                                                                   40 = x - 90x/100
                                                                   40 =  x/10
                                                                   x = 400
total no. of students = 400 

Answer 2

Answer:

x=400

Step-by-step explanation:

80%-75%=5%

85%-75%=15%

(80%+85%)/2+(5%+10%)/2=90% (Both Sub pass and Any One sub Pass students total)

total fail 100%-90%= 10%

10x/100=40

x/10=40

x=400