Question

In a combined test in Maths and Chemistry; $84\%$ candidates passed in Maths; $76\%$ in Chemistry and $8\%$ failed in both. If $340$ candidates passed in the test, then how many appeared ?

Answer 1

$\%$ of students failed in Maths $\left(n\right(A\left)\right)=100-84=16$ $\%$
$\%$ of students failed in Chemistry $\left(n\right(B\left)\right)=100-76=24$ $\%$

$\%$ of students failed in both $\left(n\right(C\left)\right)=8\%$
Total percentage of candidates which failed can be found using the formula of union of sets.
$n\left(AUB\right)=n\left(A\right)+n\left(B\right)-n\left(C\right)$
So, $n\left(AUB\right)=16+24-8=32$ $\%$
Since $32$ $\%$ of the total candidates failed, then $100-32=68$ % of candidates passed which is $=340$
$\Rightarrow \frac{68}{100}\times$ total candidates $=340$
Therefore, total candidates are $500$.