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In a certain city of 15000 families, 3.5...

In a certain city of 15000 families, 3.5% of families who read A but not B look into advertisements, 25% of the families who read B but not A look into advertisements and 50% of the families, who read both A and B look into advertisements. It is known that 8000 families read A, 4000 read B and 1000 read both A and B. The number of families who read none of the newspaper are

A

a. 3000

B

b. 4000

C

c. 6000

D

d. No family

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we will use the principle of set theory to determine the number of families who read none of the newspapers A and B. ### Step-by-Step Solution: 1. **Identify the total number of families**: - Total families in the city = 15,000. 2. **Identify the number of families reading each category**: - Families reading A = 8,000. - Families reading B = 4,000. - Families reading both A and B = 1,000. 3. **Calculate the number of families reading only A**: - Families reading only A = Families reading A - Families reading both A and B - Families reading only A = 8,000 - 1,000 = 7,000. 4. **Calculate the number of families reading only B**: - Families reading only B = Families reading B - Families reading both A and B - Families reading only B = 4,000 - 1,000 = 3,000. 5. **Calculate the total number of families reading at least one newspaper**: - Total families reading at least one newspaper = Families reading only A + Families reading only B + Families reading both A and B - Total families reading at least one newspaper = 7,000 + 3,000 + 1,000 = 11,000. 6. **Calculate the number of families reading none of the newspapers**: - Families reading none = Total families - Total families reading at least one newspaper - Families reading none = 15,000 - 11,000 = 4,000. ### Final Answer: The number of families who read none of the newspapers is **4,000**. ---
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