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JEE Main 201510 AprilOnline
Exam
JEE Main
Year
2015
Date
10 April
Mode
Online
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2015 · 10 April · Online · Mathematics · Sets and Relations

In a certain town, 25 % of the families own a phone and 15 % own a...

In a certain town, 2525 % of the families own a phone and 1515 % own a car; 6565 % families own neither a phone nor a car and 20002000 families own both a car and a phone. Consider the following three statements:

(i)5\left(i\right) 5 % families own both a car and a phone.

\left(ii\right) 35 %familiesowneitheracaroraphone.<br/><br/>(iii)40000families own either a car or a phone.<br /><br />\left(iii\right) 40000 families live in the town.

Then,

Options

  1. AOnly (ii)\left(ii\right) and (iii)\left(iii\right) are correct
  2. BOnly (i)\left(i\right) and (ii)\left(ii\right) are correct
  3. CAll (i),(ii)\left(i\right), \left(ii\right) and \left(iii\right)$ are correct
  4. DOnly (i)\left(i\right) and (iii)\left(iii\right) are correct

Correct answer

C. All (i),(ii)\left(i\right), \left(ii\right) and \left(iii\right)$ are correct

Step-by-step solution

Let set AA contains families which own a phone and set BB contain families which own a car.

If 6565 % families own neither a phone nor a car, then 3535 % will own either a phone or a car

∴n(A∪B)=35∴ n\left(A \cup B\right) = 35%

Also we know that

n(A∪B)=n(A)+n(B)−n(A∩B)n\left(A \cup B\right) = n\left(A\right) + n\left(B\right) - n ( A \cap B )

35=25+15−n(A∩B)35 = 25 + 15 - n ( A \cap B )

n(A∩B)=5n\left(A \cap B\right) = 5%

55 % families own both phone and car and it is given to be 20002000 .
∴5∴ 5%ofx = 2000

5x100=2000\dfrac{5x}{100} = 2000

x=40000x = 40000

Hence, \left(i\right), (ii)and(iii)\left(ii\right) and \left(iii\right) are correct.
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