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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:
$S_{1}$ : 5% families own both a car and a phone
$S_{2}$ : 35% families own either a car or a phone
$S_{3}$ : 40,000 families live in the town
Then, the number of statements which are true is

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answer is B.

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Detailed Solution

$n (P) = 25 %; n (C) = 15 %; n (P' \cap C') = 65 % \Rightarrow n P \cup C' = 65 %; n (P \cup C) = 35 %$

$n (P \cap C) = n (P) + n (C) - n (P \cup C) = 25 + 15 - 35 = 5 %$

Let $x$ families live in the town

$∴ x \times 5 % = 2000 \Rightarrow x = 40, 000$

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