Question

In a board exam , 53%passed in biology, 61% passed in English, 60% passed in social studies, 24% in biology & English, 35% in English and social studies 27% in biology and social studies, and 5% in none. Percentage of passes in all the three subjects is?

Answer 1

passed in Biology = 53%
passed in English = 61%
passed in social studies = 60%
passed in (bio + eng) = 24%
passed in (eng + ssc) = 35%
passed in (bio + ssc) = 27%
none passed in any subject = 5%

so, total percentage of passed students = 100% - 5% = 95%
now use formula,
n(S) = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(CnA) + n(AnBnC)

here, n(S) = 95, n(A) = 53 , n(B) = 61 , n(C) = 60
n(AnB) = 24 , n(BnC) = 35, n(CnA) = 27
Let n(AnBnC) = x

then, 95 = 53 + 61 + 60 - 24 - 35 - 27 + x
95 = 174 - 86 + x
95 = 88 + x
x = 7

hence, percentage of passed in all the three subjects is 7%