Two newspaper A and B are published in a city. It is known that 25% of city populations reads A and

English

Gujarati

Hindi

1.Set Theory

hard

Two newspaper $A$ and $B$ are published in a city. It is known that $25\%$ of the city populations reads $A$ and $20\%$ reads $B$ while $8\%$ reads both $A$ and $B$. Further, $30\%$ of those who read $A$ but not $B$ look into advertisements and $40\%$ of those who read $B$ but not $A$ also look into advertisements, while $50\%$ of those who read both $A$and $B$ look into advertisements. Then the percentage of the population who look into advertisement is

A

$12.8$

B

$13.5$

C

$13.9$

D

$13$

(JEE MAIN-2019)

Solution

Let population $=\,100$

$n(A)\, = \,25$

$n(B)\, = \,20$

$n(A \cap B)\, = \,8$

$n(A \cap \bar B)\, = \,17$

$n(\bar A \cap B)\, = \,12$

Now $\%$ of th population who look advertisement

$=\,\frac {30}{100}\times 17\,+$ $\frac {40}{100}\times 12\,+$ $\frac {50}{100}\times 8$

$=\,13.9$

Standard 11

Mathematics

Share

Similar Questions

In a class of $55$ students, the number of students studying different subjects are $23$ in Mathematics, $24$ in Physics, $19$ in Chemistry, $12$ in Mathematics and Physics, $9$ in Mathematics and Chemistry, $7$ in Physics and Chemistry and $4$ in all the three subjects. The total numbers of students who have taken exactly one subject is

medium

In a college of $300$ students, every student reads $5$ newspaper and every newspaper is read by $60$ students. The no. of newspaper is

hard

(IIT-1998)

In a class of $100$ students,$15$ students chose only physics (but not mathematics and chemistry),$3$ chose only chemistry (but not mathematics and physics), and $45$ chose only mathematics(but not physics and chemistry). Of the remaining students, it is found that $23$ have taken physics and chemistry,$20$ have taken physics and mathematics, and $12$ have taken mathematics and chemistry. The number of student who chose all the three subjects is

hard

(KVPY-2021)

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

medium

Let $\mathrm{U}$ be the set of all triangles in a plane. If $\mathrm{A}$ is the set of all triangles with at least one angle different from $60^{\circ},$ what is $\mathrm{A} ^{\prime} ?$

easy