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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 : 1) 5% families own both a car and a phone 2) 35% families own either a car or a phone. 3) 40,000 families live in the town. Which of the above statements are correct ?

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1 and 2

1 and 3

2 and 3

1, 2 and 3

answer is D.

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Detailed Solution

$n (P) = 25 %, n (C) = 15 %, n (P^{C} \cap C^{C}) = 65 %, n (P \cap C) = 2000$

Since $n (P^{C} \cap C^{C}) = 65 % \Rightarrow n (P \cup C)^{C} = 65 % \Rightarrow n (P \cup C) = 35 %$

Now $n (P \cup C) = n (P) + n (C) - n (P \cap C) \Rightarrow 35 = 25 + 15 - n (P \cap C) \Rightarrow n (P \cap C) = 40 - 35 = 5$

Thus $n (P \cap C) = 5 %, But n (P \cap C) = 2000$

$∴$ 5% of the total = 2000 $\Rightarrow$ Total number of families = $= \frac{2000 \times 100}{5} = 40000$

Since $n (P \cup C) = 35 %$ and total number of families $= 40, 000 and n (P \cap C) = 5 %$

$∴$ (1), (2) and (3) are correct.

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