Discussion
In a company with 100 employees, a survey finds that 45 read Business Today, 55 read Economic Times, and 15 read neither. How many employees read both magazines?
Answer: B
Correct answer: 15
If 15 of the 100 employees read neither magazine, then the number reading at least one is
\[n(BT \cup ET) = 100 - 15 = 85\]
Apply the inclusion–exclusion principle:
\[n(BT \cup ET) = n(BT) + n(ET) - n(BT \cap ET)\]
\[85 = 45 + 55 - n(BT \cap ET) \quad\Longrightarrow\quad n(BT \cap ET) = 100 - 85 = 15\]
So 15 employees read both.
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