In an examination,34 % of students failed in | vedclass

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(A) Let $M$ be the set of students who failed in Mathematics and $E$ be the set of students who failed in English.Given:$n(M) = 34 \%$$n(E) = 42 \%$$n

Vedclass · Accepted Answer

$44$

Vedclass · Answer

(A) Let $M$ be the set of students who failed in Mathematics and $E$ be the set of students who failed in English.Given:$n(M) = 34 \%$$n(E) = 42 \%$$n(M \cap E) = 20 \%$First,we find the percentage of students who failed in at least one subject using the formula:$n(M \cup E) = n(M) + n(E) - n(M \cap E)$$n(M \cup E) = 34 \% + 42 \% - 20 \% = 56 \%$This $56 \%$ represents the students who failed in at least one subject.The percentage of students who passed in both subjects is the complement of those who failed in at least one subject:$Percentage 	ext{ } passed = 100 \% - n(M \cup E)$$Percentage 	ext{ } passed = 100 \% - 56 \% = 44 \%$Thus,$44 \%$ of the students passed in both subjects.

In an examination,$34 \%$ of students failed in Mathematics and $42 \%$ failed in English. If $20 \%$ of the students failed in both the subjects,then the percentage of students who passed in both the subjects was:

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