In a certain town, 25 % families own a phone and 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: I. 10 % families own both a car and a phone. II. 35 % families own either a car or a phone. III. 40000 families live in the town. Which of the above statements are correct?

Step-by-step solution

Let X , P , C denote the sets of all families, families owning phone, families owning car, respectively. Draw the Venn diagram we get, n P ∪ C = 35 %   Statement II is correct. n C ∩ P = 5 % Statement I is incorrect. Let total number of families be k . Since, n P ∩ C = k × 5 100 = k 20 ⇒ 2000 = k 20 ⇒ k = 40000 ∴ Statement III is correct. ∴ It is clear from the Venn diagram that Statement II is correct. ∴ The correct answer is c .