Question

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. $54$
• C. $38$
• D. $36$

Answer 1

The correct option is D

$36$

Finding the value of :

Let $C$ be the Person who like coffee, $T$ be the Person who like tea

$\Rightarrow$$n\left(C\right)=73$, $n\left(T\right)=65$

Now, According to the question

$n(C\cup T)\le 100$

$\Rightarrow$$n\left(C\right)+n\left(T\right)-n(C\cap T)\le 100$

$\Rightarrow$ $73+65-x\le 100$

$\Rightarrow$ $x\ge 38$

Also, $73-x\ge 0$

$\Rightarrow$ $x\le 73$

$65-x\ge 0$

$\Rightarrow$ $x\le 65$

$\therefore 38\le x\le 65$

Thus, Excluding 36 all options is in between$38\le x\le 65$

$\therefore x$ cannot be $\mathbf{36}$

Hence, Option ‘D’ is Correct.