In a company with 100 employees, a survey finds that 45 read Business Today, 55 read Economic Times, and 10 read neither. How many employees read both magazines?
Answer: B
Let BT be the set of employees who read Business Today and ET be the set for Economic Times.
Total employees = 100.
Number of employees who read neither magazine = 10.
Therefore, the number of employees who read at least one magazine is n(BT ∪ ET) = 100 - 10 = 90.
Given: n(BT) = 45, n(ET) = 55.
Using the inclusion-exclusion principle:
n(BT ∪ ET) = n(BT) + n(ET) - n(BT ∩ ET)
90 = 45 + 55 - n(BT ∩ ET)
90 = 100 - n(BT ∩ ET)
n(BT ∩ ET) = 100 - 90 = 10.
So, 10 employees read both magazines.