In a company, there are 500 employees. 180 employees do not have a car. 270 employees do not have a bike and 280 employees do not have a scooter, 10 employees do not have any of the three. 420 employees have a car or a bike. 430 employees have a car or a scooter. 370 employees have a bike or a scooter.
Answers
Given : In a company, there are 500 employees. 180 employees do not have a car. 270 employees do not have a bike and 280 employees do not have a scooter, 10 employees do not have any of the three. 420 employees have a car or a bike. 430 employees have a car or a scooter. 370 employees have a bike or a scooter.
To Find : Number of employees who have all three
Solution:
C = Have Car B = Bike , S = Scooter
Total = 500
180 employees do not have a car.
=> C = 500 - 180 = 320
B = 500 - 270 = 230
S = 500 - 280 = 220
None = 10
C U B = 420
C U S = 430
B U S = 370
C ∩ B = C + B - C U B = 320 + 230 - 420 = 130
C ∩ S = C + S - C U S = 320 + 220 - 430 = 110
B ∩ S = B + S - B U S = 230 + 220 - 370 = 80
T = C + B + S - C ∩ B - C ∩ S - B ∩ S + C ∩ B ∩ S + None
=> 500 = 320 + 230 + 220 - 130 - 110 - 80 + C ∩ B ∩ S + 10
=> 500 = 460 + C ∩ B ∩ S
=> C ∩ B ∩ S = 40
Number of employees who have all three = 40
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