Mathematics - Sets and Relations Question with Solution | TestHub

Let set$A$contains families which own a phone and set$B$contain families which own a car.

If$65\%$families own neither a phone nor a car, then$35\%$will own either a phone or a car

$\therefore n\left(A\cup B\right)=35\%$

Also we know that

$n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$35=25+15-n(A\cap B)$

$n\left(A\cap B\right)=5\%$

$5\%$families own both phone and car and it is given to be$2000$.
$\therefore 5\% of x=2000$

$\frac{5x}{100} =2000$

$x=40000$

Hence,$\left(i\right), \left(ii\right)$and$\left(iii\right)$are correct.