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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 41

  • question_answer
    In a town of 10,000 families it was found that 40% family 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 number of families which buy A only is

    A) 3100               

    B) 3300

    C) 2900               

    D) 1400

    Correct Answer: B

    Solution :

    \[n(A)=40%\]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 \[10,000=200\] We want to find   \[n(A\cap {{B}^{C}}\cap {{C}^{C}})=n[A\cap {{(B\cup C)}^{C}}]\] \[=n(A)-n[A\cap (B\cup C)]\] \[=n(A)-n[(A\cap B)\cup (A\cap C)]\] \[=n(A)-[n(A\cap B)+n(A\cap C)-n(A\cap B\cap C)]\]\[=4000-[500+400-200]=4000-700=3300.\]


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