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Q.

In a certain town, 25% families own a phone and families 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. 10%  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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a

1 and 2

b

1 and 3

c

2 and 3

d

1,2 and 3

answer is C.

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Detailed Solution

n(P)=25%,n(C)=15% , nPc∩Cc=65%,n(P∩C)=2000nPc∩Cc=65%⇒ n(P∪C)c=65%⇒ n(P∪C)=35% Now n(P∪C)=n(P)+n(C)−n(P∩C)⇒ 35=25+15−n(P∩C)⇒ n(P∩C)=40−35=5⇒ 5% of the total =2000⇒  Total number of families =2000×1005=40000Therefore, statements 2 and 3 are correct.
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