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?

Question

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?

Infinity Learn · Accepted Answer

$$n(P)=25$$%,$$n(C)=15$$% , 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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