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Question

A factory has 80 workers and 3 machines. Each worker knows to operate at least two machines. If there are 65 persons who know to operate machine I, 60 for machine II and 55 for machine III, then the minimum number of persons who know to operate all the three machines is

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Solution

Let x workers know to operate all the machines.


Also, α+β+x=65
α+γ+x=60
β+γ+x=55
2(α+β+γ)+3x=180 (1)
And α+β+γ+x=80 (2)
From (1) and (2),
x=20

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