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  4. 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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Q. 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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Solution:

$C \rightarrow$ person like coffee
$T \rightarrow$ person like Tea
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$n ( C )=73$
$n ( T )=65$
$n ( C \cup T ) \leq 100$
$n ( C )+ n ( T )- n ( C \cap T ) \leq 100$
$73+65- x \leq 100$
$x \geq 38$
$73- x \geq 0 \Rightarrow x \leq 73$
$65- x \geq 0 \Rightarrow x \leq 65$
$38 \leq x \leq 65$