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,

  • Option 1)

    Only (a) and (b) are correct.

  • Option 2)

    Only (a) and (c) are correct.

  • Option 3)

     Only (b) and (c) are correct

  • Option 4)

    .  All (a), (b) and (c) are correct.

 

Answers (1)

As we learnt in

Number of Elements in Union A & B -

n (A ∪ B) = n (A) + n (B) – n (A ∩ B)

- wherein

Given A and B be any finite sets. then Number of Elements in union A & B is given by this formula.

 

Let x families live in the town according to question.

 n(P)=\frac{x\times 25}{100}=\frac{x}{4}

n(C)=\frac{x\times 15}{100}=\frac{3x}{20}

n(P\cap C)=2000

n'(P'\cap C')=x-n(P\cup C)

\frac{x\times 65}{100}=x-n(P\cup C)

=n(P\cup C)=x-\frac{x\times 65}{100}=\frac{35x}{100}=\frac{7x}{20}

Now,  according to formalue

n(P\cup C)=n(P)+n(C)-n(P\cap C)

\frac{7x}{20}=\frac{x}{4}+\frac{3x}{20}-2000

2000=\frac{8x}{20}-\frac{7x}{20}=\frac{x}{20}

\therefore\ \, x=2000\times 20=40,000 Statement 4

\therefore\ \, n(P\cap C)=2000 It is 5% of 4000

    n(P\cup C)=\frac{7}{20}\times 40000=14,000

Correct option is 4.

 

 


Option 1)

Only (a) and (b) are correct.

This is an incorrect option.

Option 2)

Only (a) and (c) are correct.

This is an incorrect option.

Option 3)

 Only (b) and (c) are correct

This is an incorrect option.

Option 4)

.  All (a), (b) and (c) are correct.

This is the correct option.

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