IIT JAM Exam > IIT JAM Questions > In a group of 265 persons, 200 like singing, ...
Start Learning for Free
In a group of 265 persons, 200 like singing, 110 like dancing and 55 like painting, if 60 person like both singing and dancing, 30 like both singing and painting and 10 like all three activities then the number of person who like only dancing and painting is
- a)20
- b)10
- c)30
- d)40
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In a group of 265 persons, 200 like singing, 110 like dancing and 55 l...
Solution: (1)
Let the number of people who like singing be n (S) = 200, who like dancing is n (D) = 110, number of people who like painting = n (P) = 55.
n (D ∪ P ∪ S) = 265
The number of people who like both singing and dancing = n (S ∩ D) = 60
The number of people who like both singing and painting = n (S ∩ P) = 30 and
The number of people who like all the 3 activities = n (D ∩ P ∩ S) = 10
n (D ∪ P ∪ S) = n (D) + n (P) + n (S) − n (D ∩ P) − n (P ∩ S) − n (S ∩ D) + n (D ∩ P ∩ S)
265 = 110 + 55 + 200 − n (D ∩ P) − 30 − 60 + 10
265 = 285 − n (D ∩ P)
n (D ∩ P) = 20
The number of persons who like dancing and painting = n (D ∩ P) − n (D ∩ P ∩ S)
= 20 − 10
= 10
Most Upvoted Answer
In a group of 265 persons, 200 like singing, 110 like dancing and 55 l...
Given:
Total number of persons (n) = 265
Number of persons who like singing (A) = 200
Number of persons who like dancing (B) = 110
Number of persons who like painting (C) = 55
Number of persons who like both singing and dancing (A∩B) = 60
Number of persons who like both singing and painting (A∩C) = 30
Number of persons who like all three activities (A∩B∩C) = 10
To find: Number of persons who like only dancing and painting (B∩C)
Solution:
Let X be the number of persons who like only singing and dancing.
Let Y be the number of persons who like only singing and painting.
Let Z be the number of persons who like only dancing and painting.
Let W be the number of persons who do not like any of the activities.
Total number of persons (n) = X + Y + Z + A∩B + A∩C + B∩C + A∩B∩C + W
We know that:
A = (A∩B) + (A∩C) + Y + (A∩B∩C)
B = (A∩B) + X + (B∩C) + (A∩B∩C)
C = (A∩C) + Y + (B∩C) + (A∩B∩C)
Substituting the given values in the above equations, we get:
200 = 60 + 30 + Y + 10
110 = 60 + X + Z + 10
55 = 30 + Y + Z + 10
Solving the above equations, we get:
Y = 100, X = 20, Z = 10
Therefore, the number of persons who like only dancing and painting (B∩C) is 10, which is option (B).
Total number of persons (n) = 265
Number of persons who like singing (A) = 200
Number of persons who like dancing (B) = 110
Number of persons who like painting (C) = 55
Number of persons who like both singing and dancing (A∩B) = 60
Number of persons who like both singing and painting (A∩C) = 30
Number of persons who like all three activities (A∩B∩C) = 10
To find: Number of persons who like only dancing and painting (B∩C)
Solution:
Let X be the number of persons who like only singing and dancing.
Let Y be the number of persons who like only singing and painting.
Let Z be the number of persons who like only dancing and painting.
Let W be the number of persons who do not like any of the activities.
Total number of persons (n) = X + Y + Z + A∩B + A∩C + B∩C + A∩B∩C + W
We know that:
A = (A∩B) + (A∩C) + Y + (A∩B∩C)
B = (A∩B) + X + (B∩C) + (A∩B∩C)
C = (A∩C) + Y + (B∩C) + (A∩B∩C)
Substituting the given values in the above equations, we get:
200 = 60 + 30 + Y + 10
110 = 60 + X + Z + 10
55 = 30 + Y + Z + 10
Solving the above equations, we get:
Y = 100, X = 20, Z = 10
Therefore, the number of persons who like only dancing and painting (B∩C) is 10, which is option (B).
|
Explore Courses for IIT JAM exam
|
|
In a group of 265 persons, 200 like singing, 110 like dancing and 55 like painting, if 60 person like both singing and dancing, 30 like both singing and painting and 10 like all three activities then the number of person who like only dancing and painting isa)20b)10c)30d)40Correct answer is option 'B'. Can you explain this answer?
Question Description
In a group of 265 persons, 200 like singing, 110 like dancing and 55 like painting, if 60 person like both singing and dancing, 30 like both singing and painting and 10 like all three activities then the number of person who like only dancing and painting isa)20b)10c)30d)40Correct answer is option 'B'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about In a group of 265 persons, 200 like singing, 110 like dancing and 55 like painting, if 60 person like both singing and dancing, 30 like both singing and painting and 10 like all three activities then the number of person who like only dancing and painting isa)20b)10c)30d)40Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a group of 265 persons, 200 like singing, 110 like dancing and 55 like painting, if 60 person like both singing and dancing, 30 like both singing and painting and 10 like all three activities then the number of person who like only dancing and painting isa)20b)10c)30d)40Correct answer is option 'B'. Can you explain this answer?.
In a group of 265 persons, 200 like singing, 110 like dancing and 55 like painting, if 60 person like both singing and dancing, 30 like both singing and painting and 10 like all three activities then the number of person who like only dancing and painting isa)20b)10c)30d)40Correct answer is option 'B'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about In a group of 265 persons, 200 like singing, 110 like dancing and 55 like painting, if 60 person like both singing and dancing, 30 like both singing and painting and 10 like all three activities then the number of person who like only dancing and painting isa)20b)10c)30d)40Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a group of 265 persons, 200 like singing, 110 like dancing and 55 like painting, if 60 person like both singing and dancing, 30 like both singing and painting and 10 like all three activities then the number of person who like only dancing and painting isa)20b)10c)30d)40Correct answer is option 'B'. Can you explain this answer?.
Solutions for In a group of 265 persons, 200 like singing, 110 like dancing and 55 like painting, if 60 person like both singing and dancing, 30 like both singing and painting and 10 like all three activities then the number of person who like only dancing and painting isa)20b)10c)30d)40Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for IIT JAM.
Download more important topics, notes, lectures and mock test series for IIT JAM Exam by signing up for free.
Here you can find the meaning of In a group of 265 persons, 200 like singing, 110 like dancing and 55 like painting, if 60 person like both singing and dancing, 30 like both singing and painting and 10 like all three activities then the number of person who like only dancing and painting isa)20b)10c)30d)40Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a group of 265 persons, 200 like singing, 110 like dancing and 55 like painting, if 60 person like both singing and dancing, 30 like both singing and painting and 10 like all three activities then the number of person who like only dancing and painting isa)20b)10c)30d)40Correct answer is option 'B'. Can you explain this answer?, a detailed solution for In a group of 265 persons, 200 like singing, 110 like dancing and 55 like painting, if 60 person like both singing and dancing, 30 like both singing and painting and 10 like all three activities then the number of person who like only dancing and painting isa)20b)10c)30d)40Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of In a group of 265 persons, 200 like singing, 110 like dancing and 55 like painting, if 60 person like both singing and dancing, 30 like both singing and painting and 10 like all three activities then the number of person who like only dancing and painting isa)20b)10c)30d)40Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a group of 265 persons, 200 like singing, 110 like dancing and 55 like painting, if 60 person like both singing and dancing, 30 like both singing and painting and 10 like all three activities then the number of person who like only dancing and painting isa)20b)10c)30d)40Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice IIT JAM tests.
|
|
Explore Courses for IIT JAM exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup