Question

in a board exam 53% passed in biology ,61% in english,60% in social studies ,24% in biology and english,35% in english and social studies,27% in biology and social studies and 5%in none percentage of passes in all the 3 subjects is
If the no of student in the class is 200 how many passed in only one subject?

Answer 1

Answer:-The number of students passed in only one subject is =60 students.

Given : In a board exam

Total number of students =200

Percentage of students passed in Biology n(A) = 53%

Percentage of students passed in English n(B)= 61%

Percentage of students passed in social studies n(C) = 60%

Percentage of students passed in biology and English n(A∩B) = 24%

Percentage of students passed in English and SST. n(B∩C)= 35%

Percentage of students passed in biology and SST. n(A∩C) = 27%

Percentage of students none passed in any subject n(A∩B∩C) = 5%

∴, the total percentage of passed students n(A∪B∪C) = 100%-n(A∩B∩C)=100% - 5% = 95%

Now we know that,

n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(C∩A) + n(A∩B∩C)

⇒ 95 = 53 + 61 + 60 - 24 - 35 - 27 +n(A∩B∩C)

⇒95 = 88+n(A∩B∩C)

⇒n(A∩B∩C)  = 7

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

Now by the figure ,(A∩B) = 24 =a+d where d=n(A∩B∩C)  = 7

n(B∩C)= 35=b+d

n(A∩C) = 27=c+d

adding all of the above

a+d+b+d+c+d=a+b+c+3d=24+35+27=86

⇒a+b+c+3(7)=86

⇒a+b+c=86-21=65%

So the percentage of students passed in only one subject is =n(A∪B∪C)-65%=95%-65%=30%

∴the number of students passed in only one subject is =30% of the total number of students= 0.30×200=60 students.