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Previous Year Question (PYQs)



In a group of 120 people:
65 eat Rice, 45 eat Bread, 42 eat Curd,
20 eat both Rice and Bread, 25 eat both Rice and Curd, 15 eat both Bread and Curd,
and 8 eat all three items.
Which of the following is the number of people who eat at least one of the three items?





Solution

Using the formula for union of three sets:
n(R ∪ B ∪ C) = n(R) + n(B) + n(C) − n(R ∩ B) − n(R ∩ C) − n(B ∩ C) + n(R ∩ B ∩ C)
Substitute:
= 65 + 45 + 42 − 20 − 25 − 15 + 8
= 152 − 60 + 8
= 100
Hence, 100 people eat at least one of the three items.


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