JEE MAIN - Mathematics (2020 - 5th September Morning Slot - No. 11)
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 :
63
36
54
38
Explanation
C $$ \to $$ person like coffee
T $$ \to $$ person like Tea
n(C) = 73
n(T) = 65
n(C $$ \cup $$ T) $$ \le $$ 100
n(C) + n(T) – n (C $$ \cap $$ T) $$ \le $$ 100
73 + 65 – x $$ \le $$ 100
x $$ \ge $$ 38
73 – x $$ \ge $$ 0 $$ \Rightarrow $$ x $$ \le $$ 73
65 – x $$ \ge $$ 0 $$ \Rightarrow $$ x $$ \le $$ 65
$$ \therefore $$ 38 $$ \le $$ x $$ \le $$ 65
T $$ \to $$ person like Tea
n(C) = 73
n(T) = 65
n(C $$ \cup $$ T) $$ \le $$ 100
n(C) + n(T) – n (C $$ \cap $$ T) $$ \le $$ 100
73 + 65 – x $$ \le $$ 100
x $$ \ge $$ 38
73 – x $$ \ge $$ 0 $$ \Rightarrow $$ x $$ \le $$ 73
65 – x $$ \ge $$ 0 $$ \Rightarrow $$ x $$ \le $$ 65
$$ \therefore $$ 38 $$ \le $$ x $$ \le $$ 65
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