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(D) Let $C$ be the set of persons who like coffee and $T$ be the set of persons who like tea.Given: $n(C) = 73$,$n(T) = 65$.Let $x$ be the percentage

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$36$

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(D) Let $C$ be the set of persons who like coffee and $T$ be the set of persons who like tea.Given: $n(C) = 73$,$n(T) = 65$.Let $x$ be the percentage of persons who like both,i.e.,$n(C \cap T) = x$.We know that the total percentage cannot exceed $100 \%$,so $n(C \cup T) \leq 100$.Using the formula $n(C \cup T) = n(C) + n(T) - n(C \cap T)$:$73 + 65 - x \leq 100$$138 - x \leq 100$$x \geq 38$.Also,the number of people who like only coffee or only tea cannot be negative:$n(C) - x \geq 0 \Rightarrow 73 - x \geq 0 \Rightarrow x \leq 73$$n(T) - x \geq 0 \Rightarrow 65 - x \geq 0 \Rightarrow x \leq 65$Combining these,we get $38 \leq x \leq 65$.Therefore,$x$ must be in the range $[38, 65]$.Among the given options,$36$ is outside this range. Thus,$x$ cannot be $36$.

$A$ survey shows that $73 \%$ of the persons working in an office like coffee,whereas $65 \%$ like tea. If $x$ denotes the percentage of them who like both coffee and tea,then $x$ cannot be

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