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1.Set Theory
medium
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
A
$63$
B
$38$
C
$54$
D
$36$
(JEE MAIN-2020)
Solution

$C \rightarrow$ person like coffee
$T \rightarrow$ person like Tea
$n(C)=73$
$n(T)=65$
$n(C \cup T) \leq 100$
$n(C)+n(T)-n(C \cap T) \leq 100$
$73+65-x \leq 100$
$x \geq 38$
$73-x \geq 0 \Rightarrow x \leq 73$
$65-x \geq 0 \Rightarrow x \leq 65$
$38 \leq x \leq 65$
Standard 11
Mathematics
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