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.
A) 10% 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.
Which of the following statements are correct

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A and B

A, B and C

A and C

B and C

answer is C.

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Detailed Solution

$\begin{array}{l} n (P) = 25 %, n (C) = 15 %; n (\bar{P} \cap \bar{C}) = 65 %, \\ n (P \cap C) = 2000 \Rightarrow n (\bar{P} \cup \bar{C}) = 65 % \\ n (P \cup C) = 35 % \Rightarrow n (P \cap C) = 5 % \\ ∴ 5 % of the total = 2000 \end{array}$
$\Rightarrow$ total number of familyes $= \frac{2000 \times 100}{5} = 40000$