Question

In a certain office, $72$% of the workers prefer tea and $44$% prefer coffee. If each of them prefers tea or coffee and $40$ like both, the total number of workers in the office is:

• A. $200$
• B. $240$
• C. $250$
• D. $320$

Answer 1

The correct option is C $250$

$\left(T\right)$ Tea $=72\%$

$\left(C\right)$ Coffee $44\%$

$T\cap C\Rightarrow 40$

$T\cup C=T+C-(T\cap C)$

$T\cup C=72\%+44\%-40$

$\Rightarrow 100\%=72\%+44\%-40$

$\Rightarrow -116\%+100\%=-40$

$\Rightarrow 16\%=40$

$\Rightarrow 1\%=\frac{40}{16}$

$\Rightarrow 100\%=\frac{40}{16}\times 100=250$