In a combined test in English and Physics; $36 %$ candidates failed in English; $28 %$ failed in Physics and $12 %$ in both; find the total number of candidates appeared, if $208$ candidates have failed.

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Solution

No. of students failed in English $(n (A)) = 36 %$
No. of students failed in Physics $(n (B)) = 28 %$
No. of students failed in Both $(n (C)) = 12 %$
Total percentage of candidates which failed can be found using the formula of union of sets
$n (A U B) = n (A) + n (B) - n (C)$
So, $n (A U B) = 36 + 28 - 12 = 52$ $%$
Since $52$ $%$ of the total candidates failed, which is $= 208$
$\Rightarrow \frac{52}{100} \times$ total candidates $= 208$
$∴$ Total candidates $= 400$

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In a combined test in English and Physics; 36% candidates failed in English; 28% failed in Physics and 12% in both; find the total number of candidates appeared, if 208 candidates have failed.

In a combined test in English and Physics; $36 %$ candidates failed in English; $28 %$ failed in Physics and $12 %$ in both; find the total number of candidates appeared, if $208$ candidates have failed.