Subjective Type

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.

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
$$ n(AUB) = n(A) + n (B) - n(C) $$
So, $$ n(AUB) = 36 + 28 - 12 = 52 $$ $$\%$$
Since $$ 52 $$ $$\%$$ of the total candidates failed, which is $$ = 208 $$
$$ \Rightarrow \dfrac {52}{100} \times $$ total candidates $$ = 208 $$
$$\therefore$$ Total candidates $$= 400 $$

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