Question

In a certain town, $25\%$ of the families own a phone and $15\%$ own a car; $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone. Consider the following three statements :
(a) $5\%$ families own both a car and a phone
(b) $35\%$ families own either a car or a phone
(c) $40,000$ families live in the town
Then,

• A. Only (b) and (c) are correct
• B. Only (a) and (c) are correct
• C. All (a), (b) and (c) are correct
• D. Only (a) and (b) are correct

Answer 1

The correct option is C All (a), (b) and (c) are correct

Let P,C be the set of families who own phone and car respectively as shown in venn diagram below,
Let $x$% families own both
$\Rightarrow 25-x+x+15-x+65=100\Rightarrow x=5$
So, statement (a) is correct.

Now, families own either car or phone $=25-x+15-x+x=35$
So,statement (b) is correct.


also $2,000$ families own both a car and a phone.
$\text{So, total no. of families =}\frac{100}{5}\times 2000=40000$
Hence, statement (c) is correct.