Question

In an examination, $42\%$ students failed in mathematics and $52\%$ failed in science. If $17\%$ failed in both the subjects, find the percentage of those who passed in both the subjects.

Answer 1

The percentage of students who failed in mathematics $=42$

The percentage of students who failed science$=52$

The percentage of students who failed in both subjects $=17$

$n\left(M\right)=42$

$n\left(S\right)=52$

$n\left(B\right)=17=n(M\cap S)$

$n(M\cup S)=n\left(M\right)+n\left(S\right)-n\left(B\right)$

$=42+52-17$

$=94-17$

$=77$

The percentage of students who passed both subjects$=100-77=23\%$