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Question

A group of 123 workers went to a canteen for cold drink, ice-cream and tea. 42 workers took ice-cream, 36 took tea and 30 took cold drink. 15 workers purchased ice-cream and tea, 10 purchased ice-cream and cold drink, and 4 purchased cold drink and tea but not ice-cream. Then the number of workers who did not purchase anything is

A
60
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B
79
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C
44
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D
40
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Solution

The correct option is C 44
Let C,I and T denote the set of workers who purchased cold drink, ice-cream and tea respectively.
n(U)=123
n(I)=42,n(T)=36,n(C)=30
n(IT)=15,n(IC)=10
n(CTI)=4
n(CTI)=4=n(CT)n(CTI)

Number of workers who did not purchase anything
=n(CTI)
=n(U)n(CTI)
=n(U)[n(I)+n(T)+n(C)n(IT)n(IC)n(CT)+n(CTI)]
=123[42+36+3015104]
n(CTI)=44

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n(A∪B∪C) = n(A) + n(B) + n(C) − n(A∩B) − n(B∩C) − n(C∩A) + n(A∩B∩C)
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