In a group of 120 people: 65 eat Rice, 45 eat bread, 42 eat curd, 20 eat both…
2025
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:
- A.
56
- B.
100
- C.
92
- D.
65
Attempted by 204 students.
Show answer & explanation
Correct answer: B
Key idea: use the inclusion–exclusion principle to avoid double-counting.
Step 1: Sum the individual counts: 65 + 45 + 42 = 152.
Step 2: Subtract pairwise overlaps (to remove double-counting): 20 + 25 + 15 = 60.
Step 3: Add back the triple overlap (was subtracted three times in step 2 but should be counted once): +8.
Final calculation: 152 − 60 + 8 = 100.
Therefore, the number of people who eat at least one of the three items is 100.
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