Question

In a certain town 30% families own a scooter and 40% on a car 50% own neither a scooter nor a car 2000 families own both a scooter and car consider the following statements in this regard 

(1) 20% families own both scooter and car 

(2) 35% families own either a car or a scooter 

(3) 10000 families live in town Which of the above statement are correct? 

(a) 2 and 3 

(b) 1, 2 and 3 

(c) 1 and 2 

(d) 1 and 3

Answer 1

The correct option (d) 1 and 3

Explanation:

Suppose x families live in the town 

A = {families have scooter} 

B = {families have car} 

∴ n(A) = 30x/100  n(B) = 40x/100 x and n(A ∪ B)' = 50x/100

∴ n(A ∪ B) = 50x/100 

∴ n(A ∩ B) = 20x/100

∴ 20x/100 = 2000 

∴ x = 10000

∴ both scooter and car have 20 %