Subjective Type

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 ?

Solution

$$\%$$ of students failed in Maths $$( n(A) )= 100 - 84 = 16 $$ $$\%$$ $$\%$$ of students failed in Chemistry $$( n(B) ) = 100 - 76 = 24 $$ $$\%$$ $$\%$$ of students failed in both $$( n(C) ) = 8 \%$$ 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, $$ n(AUB) = 16 + 24 - 8 = 32 $$ $$\%$$ Since $$ 32 $$ $$\%$$ of the total candidates failed, then $$ 100 - 32 = 68 $$ % of candidates passed which is $$ = 340 $$ $$ \Rightarrow \dfrac {68}{100} \times $$ total candidates $$ = 340 $$ Therefore, total candidates are $$ 500 $$.

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