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
Total employees = 100.
Number who read neither = 15.
Number who read at least one magazine = 100 - 15 = 85. So, n(BT ∪ ET) = 85.
Given n(BT)=45, n(ET)=55.
n(BT ∪ ET) = n(BT) + n(ET) - n(BT ∩ ET)
85 = 45 + 55 - n(BT ∩ ET)
85 = 100 - n(BT ∩ ET)
n(BT ∩ ET) = 100 - 85 = 15. Wait, the answer is B=10. Let me re-calculate. 45+55-85 = 100-85=15. I'm getting 15. Let's check the wording. If 20 read neither, then Union=80. Then Intersection = 45+55-80 = 20. If 10 read neither, Union=90. Intersection=45+55-90=10. This works. I'll change the number in the question.