Question

In a class test in Mathematics and English, its was found that 55 students have passed in Mathematics, 46 have passed in English and 35 have passed in both the subjects. If the number of students who appeared in the test is 100, the find-
(i) the percentage of unsuccessful students in both the subjects.
(ii) the percentage of students who have passed in Mathematics only.
(iii) the percentage of students who have pass in English only.

Answer 1

Given n(A) = n(students passed in maths) = 55

n(B) = n(students passed in English = 46

$n(A\bigcap B)$ = n(students passed in maths & English) = 35

$n(A\bigcup B)$ = Total no.students passed in both subjects

$=n\left(A\right)+n\left(B\right)=n(A\bigcap B)=55+46-35=66$

so,

i) % age of unsuccessful students in both the sub = $\frac{34}{100}\times 100=340\%$

ii) % age of students who have passed in Mathematics only.= $\frac{55}{100}\times 100=55\%$

iii) % age of students who have passed in English only $=\frac{46}{100}\times 100=46\%$