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Question

In a certain town, 25% of the families own a phone and 15% own a car; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements :
(a) 5% families own both a car and a phone
(b) 35% families own either a car or a phone
(c) 40,000 families live in the town
Then,

A
Only (b) and (c) are correct
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B
Only (a) and (c) are correct
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C
All (a), (b) and (c) are correct
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D
Only (a) and (b) are correct
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Solution

The correct option is C All (a), (b) and (c) are correct
Let P,C be the set of families who own phone and car respectively as shown in venn diagram below,
Let x% families own both
25x+x+15x+65=100x=5
So, statement (a) is correct.

Now, families own either car or phone =25x+15x+x=35
So,statement (b) is correct.


also 2,000 families own both a car and a phone.
So, total no. of families = 1005×2000=40000
Hence, statement (c) is correct.



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