Question:
In a group of people it was observed that 86 persons know Odia, 64 know English, 42 know Hindi, 39 know Odia and English, 21 know English and Hindi, 17 know Odia and English, and 16 persons know all the three languages. How many persons in the group know at least one language?
In a group of people it was observed that 86 persons know Odia, 64 know English, 42 know Hindi, 39 know Odia and English, 21 know English and Hindi, 17 know Odia and English, and 16 persons know all the three languages. How many persons in the group know at least one language?
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Use the inclusion-exclusion principle to calculate the total number of elements in overlapping sets.
Updated On: Feb 3, 2026
- 131
- 99
- 192
- None of the above
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The Correct Option is B
Solution and Explanation
Step 1: Applying the principle of inclusion and exclusion.
Let the total number of people be \( N \). We can calculate \( N \) using the inclusion-exclusion principle: \[ N = (86 + 64 + 42) - (39 + 21 + 17) + 16 \]
Step 2: Substituting values.
\[ N = (86 + 64 + 42) - (39 + 21 + 17) + 16 = 192 - 77 + 16 = 131 \]
Step 3: Conclusion.
Thus, the number of people who know at least one language is (2) 99.
Let the total number of people be \( N \). We can calculate \( N \) using the inclusion-exclusion principle: \[ N = (86 + 64 + 42) - (39 + 21 + 17) + 16 \]
Step 2: Substituting values.
\[ N = (86 + 64 + 42) - (39 + 21 + 17) + 16 = 192 - 77 + 16 = 131 \]
Step 3: Conclusion.
Thus, the number of people who know at least one language is (2) 99.
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