
A group of 123 workers went to a canteen for coffee, ice-cream and tea. 42 workers took ice-cream, 36 took tea and 30 took coffee, 15 workers purchased ice-cream and tea, 10 ice-cream and coffee and 4 coffee and tea but not ice-cream, while 11 took ice-cream and tea but not coffee. Determine how many workers did not purchase anything?
Answer
491.4k+ views
Hint: We will proceed in this problem by making a venn diagram of the problem.
Let consider three sets i.e., , and which represents the workers purchasing coffee, ice-cream and tea respectively.
Complete step-by-step answer:
Number of workers purchasing ice-cream,
Number of workers purchasing tea,
Number of workers purchasing coffee,
Number of workers purchasing ice-cream and tea,
Number of workers purchasing ice-cream and coffee,
Number of workers purchasing only ice-cream and tea but not coffee (shown in the figure through blue coloured hatched lines) is given by
Number of workers purchasing only coffee and tea but not ice-cream (shown in the figure through green coloured hatched lines) is given by
As we know that for any three sets i.e., , and , we can write
Now substituting all the values in equation (1), we get
Number of workers purchasing either ice-cream or tea or coffee is given by
Since, Number of workers who did not purchase anything is equal to the total number of workers minus the number of workers purchasing either ice-cream or tea or coffee.
.
Note: In these types of problems, a venn diagram is used to calculate all the unknowns. In this particular problem, we used the given data to determine the unknowns in equation (1).
Let consider three sets i.e.,
Complete step-by-step answer:

Number of workers purchasing ice-cream,
Number of workers purchasing tea,
Number of workers purchasing coffee,
Number of workers purchasing ice-cream and tea,
Number of workers purchasing ice-cream and coffee,
Number of workers purchasing only ice-cream and tea but not coffee (shown in the figure through blue coloured hatched lines) is given by
Number of workers purchasing only coffee and tea but not ice-cream (shown in the figure through green coloured hatched lines) is given by
As we know that for any three sets i.e.,
Now substituting all the values in equation (1), we get
Number of workers purchasing either ice-cream or tea or coffee is given by
Since, Number of workers who did not purchase anything is equal to the total number of workers minus the number of workers purchasing either ice-cream or tea or coffee.
Note: In these types of problems, a venn diagram is used to calculate all the unknowns. In this particular problem, we used the given data to determine the unknowns in equation (1).
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