In an examination,30 % of the total students | vedclass

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Question

(C) Let the total number of students be $100$.Let $H$ be the set of students who failed in Hindi and $E$ be the set of students who failed in English.

Vedclass · Accepted Answer

$45$

Vedclass · Answer

(C) Let the total number of students be $100$.Let $H$ be the set of students who failed in Hindi and $E$ be the set of students who failed in English.Given: $n(H) = 30$,$n(E) = 45$,and $n(H \cap E) = 20$.We need to find the number of students who failed in at least one subject,which is given by the union $n(H \cup E)$.Using the formula: $n(H \cup E) = n(H) + n(E) - n(H \cap E)$.$n(H \cup E) = 30 + 45 - 20 = 55$.So,$55 \%$ of students 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 passed $= 100 \% - 55 \% = 45 \%$.

In an examination,$30 \%$ of the total students failed in Hindi,$45 \%$ failed in English,and $20 \%$ failed in both the subjects. Find the percentage of those who passed in both the subjects. (in $\%$)

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