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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 where as 13 persosn speak both Kannada and English. How many people speak all the three languages ?
- a)6
- b)7
- c)8
- d)9
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In a room containing 28 people, there are 18 people who speak English,...
Let X was the people who speaks all three languages.
Total number of people = (Hindi + English + Kannad) - (Hindi and English + Hindi and Kannad + Kannad and English) + X
Total number of people = (Hindi + English + Kannad) - (Hindi and English + Hindi and Kannad + Kannad and English) + X
28 = (15 + 22 + 18) - (9 + 11 + 13) +X
X = 28 - 55 + 33
X = 6.
Most Upvoted Answer
In a room containing 28 people, there are 18 people who speak English,...
Given information:
- Total number of people in the room = 28
- Number of people who speak English = 18
- Number of people who speak Hindi = 15
- Number of people who speak Kannada = 22
- Number of people who speak both English and Hindi = 9
- Number of people who speak both Hindi and Kannada = 11
- Number of people who speak both Kannada and English = 13
To find: How many people speak all three languages?
Solution:
To find the number of people who speak all three languages, we need to find the intersection of all three sets, i.e., English, Hindi, and Kannada.
Let us first find the number of people who speak only English:
Number of people who speak only English = Total number of people who speak English - (Number of people who speak both English and Hindi + Number of people who speak both English and Kannada) + Number of people who speak all three languages
= 18 - (9 + 13) + Number of people who speak all three languages
= 18 - 22 + Number of people who speak all three languages
= -4 + Number of people who speak all three languages
Similarly, we can find the number of people who speak only Hindi and only Kannada:
Number of people who speak only Hindi = 15 - (9 + 11) + Number of people who speak all three languages
= 15 - 20 + Number of people who speak all three languages
= -5 + Number of people who speak all three languages
Number of people who speak only Kannada = 22 - (13 + 11) + Number of people who speak all three languages
= 22 - 24 + Number of people who speak all three languages
= -2 + Number of people who speak all three languages
Now, we know that the total number of people in the room is 28. Therefore, the number of people who speak at least one of the three languages is:
Number of people who speak at least one language = Number of people who speak only English + Number of people who speak only Hindi + Number of people who speak only Kannada + Number of people who speak both English and Hindi + Number of people who speak both Hindi and Kannada + Number of people who speak both Kannada and English
= (-4 + Number of people who speak all three languages) + (-5 + Number of people who speak all three languages) + (-2 + Number of people who speak all three languages) + 9 + 11 + 13
= 22 + 3*Number of people who speak all three languages
We know that the total number of people who speak at least one language is 28. Therefore,
22 + 3*Number of people who speak all three languages = 28
3*Number of people who speak all three languages = 6
Number of people who speak all three languages = 2
Therefore, the correct option is (A) 6.
- Total number of people in the room = 28
- Number of people who speak English = 18
- Number of people who speak Hindi = 15
- Number of people who speak Kannada = 22
- Number of people who speak both English and Hindi = 9
- Number of people who speak both Hindi and Kannada = 11
- Number of people who speak both Kannada and English = 13
To find: How many people speak all three languages?
Solution:
To find the number of people who speak all three languages, we need to find the intersection of all three sets, i.e., English, Hindi, and Kannada.
Let us first find the number of people who speak only English:
Number of people who speak only English = Total number of people who speak English - (Number of people who speak both English and Hindi + Number of people who speak both English and Kannada) + Number of people who speak all three languages
= 18 - (9 + 13) + Number of people who speak all three languages
= 18 - 22 + Number of people who speak all three languages
= -4 + Number of people who speak all three languages
Similarly, we can find the number of people who speak only Hindi and only Kannada:
Number of people who speak only Hindi = 15 - (9 + 11) + Number of people who speak all three languages
= 15 - 20 + Number of people who speak all three languages
= -5 + Number of people who speak all three languages
Number of people who speak only Kannada = 22 - (13 + 11) + Number of people who speak all three languages
= 22 - 24 + Number of people who speak all three languages
= -2 + Number of people who speak all three languages
Now, we know that the total number of people in the room is 28. Therefore, the number of people who speak at least one of the three languages is:
Number of people who speak at least one language = Number of people who speak only English + Number of people who speak only Hindi + Number of people who speak only Kannada + Number of people who speak both English and Hindi + Number of people who speak both Hindi and Kannada + Number of people who speak both Kannada and English
= (-4 + Number of people who speak all three languages) + (-5 + Number of people who speak all three languages) + (-2 + Number of people who speak all three languages) + 9 + 11 + 13
= 22 + 3*Number of people who speak all three languages
We know that the total number of people who speak at least one language is 28. Therefore,
22 + 3*Number of people who speak all three languages = 28
3*Number of people who speak all three languages = 6
Number of people who speak all three languages = 2
Therefore, the correct option is (A) 6.
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In a room containing 28 people, there are 18 people who speak English,...
6
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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 where as 13 persosn speak both Kannada and English. How many people speak all the three languages ?a)6b)7c)8d)9Correct answer is option 'A'. Can you explain this answer?
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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 where as 13 persosn speak both Kannada and English. How many people speak all the three languages ?a)6b)7c)8d)9Correct answer is option 'A'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about 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 where as 13 persosn speak both Kannada and English. How many people speak all the three languages ?a)6b)7c)8d)9Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 where as 13 persosn speak both Kannada and English. How many people speak all the three languages ?a)6b)7c)8d)9Correct answer is option 'A'. Can you explain this answer?.
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