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  4. In a certain town 25 % families own a cell phone, 15 % families own a scooter and 65 % families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is

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Q. In a certain town $25\%$ families own a cell phone, $15\%$ families own a scooter and $65\%$ families own neither a cell phone nor a scooter. If $1500$ families own both a cell phone and a scooter, then the total number of families in the town is

KEAMKEAM 2008Sets

Solution:

Let the total population of town be $ x $ .

$ \therefore $ $ \frac{25x}{100}+\frac{15x}{100}-1500+\frac{65x}{100}=x $
$ \Rightarrow $ $ \frac{105x}{100}-x=1500 $
$ \Rightarrow $ $ \frac{5x}{100}=1500 $
$ \Rightarrow $ $ x=30000 $

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