Question

In a certain town , $25$% families own a phone and $15$% own a car, $65$% families own neither a phone nor a car. $2000$ families own both a car and a phone. Consider the following statements in this regard.
I) 10% families own both a car and a phone
II) 35% families own either a car or a phone
III) 40,000 families live in the town.
Which of the above statements are correct ?

• A. $I$ & $II$
• B. $I$ & $III$
• C. $II$ & $III$
• D. $I$,$II$ & $III$

Answer 1

The correct option is C $II$ & $III$

$n(C\cup P)=n\left(C\right)+n\left(P\right)-n(C\cap P)+x\left(neither\right)$
$100=25+15-n(C\cap P)+x\left(neither\right)$
$100=25+15-n(C\cap P)+65$
$n(C\cap P)=5\%$
Let Total no of families$=a$
$\therefore a\times 5$$\%$$=2000$
$a=40000$
either a phone or a car$=100-neither$
$=100-65$
$=35\%$