Question

In an examination $82\%$ of the candidates passed in Maths, $72\%$ passed in Science and $55\%$ passed in both. Find the percentage of students failed in both.
(Draw Venn diagram to verify)

Answer 1

Number of candidates appeared for examination $=n(\cup )=100$

Number of candidates passed in Maths$=n\left(M\right)=82\%$

Number of candidates passed in Science$=n\left(S\right)=72\%$

Number of candidates passed in both $=n(M\cap S)=55\%$

Total number of candidates passed $=n(M\cup S)$

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

$82\%$$+72\%$$-55\%$

$=99\%$

$\therefore$ Number of failed candidates

$=n(\cup )-n(M\cup S)$

$=100-99$

$=1\%$