# A survey shows that $\inline 73\; ^{o}/_{o}$ of the persons working in an office like coffee, whereas $\inline 65\; ^{o}/_{o}$ like tea. If $\inline x$ denotes the percentage of them, who like both coffee and tea, then $\inline x$ cannot be : Option: 1 Option: 2 Option: 3 Option: 4

\begin{aligned} &\mathrm{C} \rightarrow \text { person like coffee }\\ &\mathrm{T} \rightarrow \text { person like Tea }\\ &n(C)=73\\ &\mathrm{n}(\mathrm{T})=65\\ &n(C \cup T) \leq 100\\ &\mathrm{n}(\mathrm{C})+\mathrm{n}(\mathrm{T})-\mathrm{n}(\mathrm{C} \cap \mathrm{T}) \leq 100 \end{aligned}

$\\73+65-x \leq 100 \\ x \geq 38 \\ 73-x \geq 0 \Rightarrow x \leq 73 \\ 65-x \geq 0 \Rightarrow x \leq 65 \\ 38 \leq x \leq 65$

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