Question

In a town of 10000 families, it was found that $40 \%$ families buy newspaper $A, 20 \%$ buy newspaper $B$ and $10 \%$ families buy newspaper $C, 5 \%$ families buy $A$ and $B, 3 \%$ buy $B$ and $C$ and $4 \%$ buy $A$ and $C$. If $2 \%$ families buy all the three newspapers, then the number of families which buy $A$ only is

• A. 3100
• B. 3300
• C. 2900
• D. 1400

Answer 1

Answer: (B)

$n(A)=40 \%$ of $10,000=4,000$
$n(B)=20 \%$ of $10,000=2,000$
$n(C)=10 \%$ of $10,000=1,000$
$n(A \cap B)=5 \%$ of $10,000=500$
$n(B \cap C)=3 \%$ of $10,000=300$
$n(C \cap A)=4 \%$ of $10,000=400$
$n(A \cap B \cap C)=2 \%$ of $10,000=200$

from the above Venn diagram, number of families which buy newspaper $A$ only $=3300$