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Properties of Set Operation

There are 80 ...

Question

There are $80$ families in a small town extension area. $20 %$ of these families own a car each. $50 %$ of the remaining families own a motor cycle each. Let $N$ families in that extension do not own any vehicle. Then the value of $\frac{N}{4}$ is

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Solution

$n (Family owning car) = 20 % of 80 = 16 n (m) = 50 % of remaining = 32 n (C^{c} \cap M^{c}) = 80 - (16 + 32) = 32 N = 32 \Rightarrow \frac{N}{4} = 8$

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