In a combined test in Maths and Chemistry; 84% candidates passed in Maths; 76% in Chemistry and 8% failed in both. Find the percentage of failed candidates.

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Solution

% of students failed in Maths, $n (A) = 100 - 84 = 16$ %
% of students failed in Chemistry, $n (B) = 100 - 76 = 24$ %
% failed in both, $n (C) = 8 %$

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, $n (A U B) = 16 + 24 - 8 = 32$ %

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In a combined test in Maths and Chemistry; 84% candidates passed in Maths; 76% in Chemistry and 8% failed in both. Find the percentage of failed candidates.

% of students failed in Maths, n(A)=100−84=16 % % of students failed in Chemistry, n(B)=100−76=24 % % failed in both, n(C)=8%Total percentage of candidates which failed can be found using the formula of union of setsn(AUB)=n(A)+n(B)−n(C)So, n(AUB)=16+24−8=32 %