Question

In an exam, $27\%$ students failed in Maths, $24\%$ students failed in English and $20\%$ students failed in both the subjects.
i) Find the percentage of students who failed in any of the subjects.
ii) Find the percentage of students who passed in both the subjects.
iii) If $414$ students passed in both the subjects, find the total number of students.

Answer 1

$n\left(A\right)=27,n\left(B\right)=24,n(A\bigcap B)=20$

i) $n(A\bigcup B)=27+24-20$

$=31$%

ii) $n\left(\overline{A\bigcup B}\right)=100-31=69$%

iii) $69$% of x$=414$

$\Rightarrow \frac{69}{100}\times x=414\Rightarrow x=\frac{414\times 100}{69}$

$=600$