In a room containing 28 people, there are 18 people who speak English, 15…
1998
In a room containing 28 people, there are 18 people who speak English, 15 people who speak Hindi and 22 people who speak Kannada. 9 persons speak both English and Hindi, 11 persons speak both Hindi and Kannada whereas 13 persons speak both Kannada and English. How many people speak all the three languages?
Answer: D. 6 — To find the number of people who speak all three languages, we apply the Principle of Inclusion-Exclusion for three sets. Let E, H, and K represent the sets…
- A.
9
- B.
8
- C.
7
- D.
6
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Correct answer: D
To find the number of people who speak all three languages, we apply the Principle of Inclusion-Exclusion for three sets. Let E, H, and K represent the sets of people speaking English, Hindi, and Kannada respectively.
The total number of people in the room is given by the formula: Total = |E| + |H| + |K| - (|E∩H| + |H∩K| + |K∩E|) + |E∩H∩K|.
Substituting the given values: 28 = 18 + 15 + 22 - (9 + 11 + 13) + x, where x is the number of people speaking all three languages.
Simplifying the equation: 28 = 55 - 33 + x, which becomes 28 = 22 + x. Solving for x gives x = 6.
Therefore, 6 people speak all three languages.
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