A toy factory has three machines A, B & C and 240 workers. Each worker knows to operate at least one of the three machines. If there are 195 persons who know how to operate machine A, 180 who know how to operate machine B and 165 who know how to operate machine C, 120 know how to operate machine A & B , 125 know how to operate machine B & C , 130 know how to operate machine A & C . How many workers know how to operate all these three machines?
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Let A be the set of people who know how to operate machine 1
Let B be the set of people who know how to operate machine 2
Let C be the set of people who know how to operate machine 3
A∪B∪C = A + B + C - (A n B + B n C + C n A) + (A n B n C)
240 = 195 + 180 + 165 – ( 120 + 125 + 130) + x
X = 75
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Let A be the set of people who know how to operate machine 1
Let B be the set of people who know how to operate machine 2
Let C be the set of people who know how to operate machine 3 .
A U B U C = A + B + C - (A n B + B n C + C n A) + (A n B n C)
240 = 195 + 180 + 165 – ( 120 + 125 + 130) + x
x = 75
Therefore, numbers of workers are 75.
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