In a certain town, 25 % families own a phone and 15 % own a car, 65...

Let $X, P, C$ denote the sets of all families, families owning phone, families owning car, respectively.

Draw the Venn diagram

we get,~

$n\left(P \cup C\right) = 35$

Statement~$II$~is correct.

$n\left(C \cap P\right) = 5$~

Statement~$I$ is incorrect.~

Let total number of families be $k$.~

Since, $n\left(P \cap C\right) = \dfrac{k \times 5}{100} = \dfrac{k}{20} ⇒ 2000 = \dfrac{k}{20}$

$⇒ k = 40000$

$∴$ Statement $III$~is correct.

$∴$ It is clear from the Venn diagram that Statement II is correct.

$∴$ The correct answer is \left(c\right)$.</p></blockquote>$