Question:
In a flight 50 people speak Hindi, 20 speak English and 10 speak both English and Hindi. The number of people who speak at least one of the two languages is:
In a flight 50 people speak Hindi, 20 speak English and 10 speak both English and Hindi. The number of people who speak at least one of the two languages is:
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You can verify this with a Venn Diagram. Place 10 in the intersection. Then Hindi-only speakers are \( 50 - 10 = 40 \), and English-only speakers are \( 20 - 10 = 10 \). Total: \( 40 + 10 + 10 = 60 \).
Updated On: May 1, 2026
- 40
- 50
- 20
- 80
- 60
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Solution and Explanation
Concept: The problem asks for the number of people in the union of two sets. According to the Principle of Inclusion-Exclusion, the number of elements in the union of two sets \( A \) and \( B \) is given by: \[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \] This prevents "double-counting" the individuals who belong to both categories.
Step 1: Identify the given set values.
Let \( H \) be the set of Hindi speakers and \( E \) be the set of English speakers.
• \( n(H) = 50 \)
• \( n(E) = 20 \)
• \( n(H \cap E) = 10 \)
Step 2: Apply the Inclusion-Exclusion formula.
The number of people who speak at least one language is \( n(H \cup E) \): \[ n(H \cup E) = 50 + 20 - 10 \] \[ n(H \cup E) = 70 - 10 = 60 \]
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