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
Answer (as printed): C
Explanation
Let total number be $x$. Then, $$\begin{aligned} & n(A)=\frac{72}{100} x=\frac{18 x}{25}, n(B)=\frac{44}{100} x=\frac{11 x}{25} \text { and } n(A \cap B)=40 . \\ & n(A \cup B)=n(A)+n(B)-n(A \cap B) \\ & \Rightarrow \quad x=\frac{18 x}{25}+\frac{11 x}{25}-40 \Rightarrow \frac{29 x}{25}-x=40 \\ & \Rightarrow \quad \frac{4 x}{25}=40 \Rightarrow x=250 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.