Question

Two newspapers $A$ and $B$ are published in a city. It is known that $30\%$ of the city population read $A$ and $25\%$ read $B$, while $10\%$ read both $A$ and $B$. Further, $20\%$ of those who read $A$ but not $B$ look into sports news and $40\%$ of those who read $B$ but not $A$ also look into sports news, while $50\%$ of those who read both $A$ and $B$ look into sports news. Then the percentage of the population who look into sport news, is

• A. $15$
• B. $13$
• C. $17.5$
• D. $12.7$

Answer 1

The correct option is A $15$

Let the population of the city be $100$.
Then $n\left(A\right)=30,n\left(B\right)=25,n(A\cap B)=10$


Percentage of population who look into sports news
$=\frac{20}{100}\times n(A\cap B^{\prime })+\frac{40}{100}\times n(B\cap A^{\prime })+\frac{50}{100}\times n(A\cap B)=\frac{1}{100}\left[\right(20\times 20)+(40\times 15)+(50\times 10\left)\right]=15\%$