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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