in a certain town 25% families own a cell phone 15% familesown a scooter and 65% families own neither a cell phone nor a scooter if 500 families own both a cell phone and a scooter, then the total number of families in the town is

Options

A. 1 and 2
B. 1 and 3
C. 2 and 3
D. 1,2 and 3

Explanation

Let there be x families in the town .Let P and C denote the set of families using phone and car respectively. Then ,
`n(P) =(25x)/(100)=(x)/(4),n( C) =(15x)/(100)=(3x)/(20)`
` and ,n(barPcapbarC)=(65x)/(100)=(13x)/(20)`
Also `n(Pcap c) = 2000.`
Now ,
`n (barPcap barC)=(13x)/(20)`
` implies n(bar(P capC))=(13x)/(20)`
`implies n(U)-n(P cup C)=(13x)/(20)`
`implies x-{n(P)+n( C) -n(P cap C)=(13x)/(20)`
`implies x-((x)/(4)+(3x)/(20)-2000)=(13x)/20)implies 2000implies x x= 40000`
thus ,statement 3 is true
10% of the total familes in the town is 4000 and it is given that 2000 familie own both a car and a Phone ,SO statement 1 is not true .
NOw,
`n(Pcup C)=n(P)+n(C)-n(PcapC)`
`implies n(Pcup C)+(x)/(4)+(3x)/(20)-2000`
`implies n(pcup C)= 10000+600-2000=14000`
`implies n(P cup C) = 35% of 40000`
thus ,statement 3 is correct.