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 :
Solution
C $\to$ person like coffee
<br><br>T $\to$ person like Tea
<br><br>n(C) = 73
<br><br>n(T) = 65
<br><br>n(C $\cup$ T) $\le$ 100
<br><br>n(C) + n(T) – n (C $\cap$ T) $\le$ 100
<br><br>73 + 65 – x $\le$ 100
<br><br>x $\ge$ 38
<br><br>73 – x $\ge$ 0 $\Rightarrow$ x $\le$ 73
<br><br>65 – x $\ge$ 0 $\Rightarrow$ x $\le$ 65
<br><br>$\therefore$ 38 $\le$ x $\le$ 65
About this question
Subject: Mathematics · Chapter: Sets, Relations and Functions · Topic: Sets and Operations
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