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 $=3300$