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In a class of 30 pupils, 12 take needle work, 16 take Physics and 18 take History. If all the 30 students take atleast one subject and no one takes all three, then the number of pupils taking 2 subjects is
- a)16
- b)6
- c)8
- d)20
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In a class of 30 pupils, 12 take needle work, 16 take Physics and 18 t...
Given, n(N) = 12, n(P) = 16, n(H)
Therefore,
Now, number of pupils taking two subjects
= 16 - 0 =16
Therefore,
Now, number of pupils taking two subjects
= 16 - 0 =16Most Upvoted Answer
In a class of 30 pupils, 12 take needle work, 16 take Physics and 18 t...
Given:
- Total number of pupils in the class = 30
- Number of pupils taking Needle work = 12
- Number of pupils taking Physics = 16
- Number of pupils taking History = 18
- All students take at least one subject
- No student takes all three subjects
To find:
- The number of pupils taking two subjects
Solution:
To find the number of pupils taking two subjects, we need to consider the overlapping areas of the subjects.
Step 1: Finding the number of pupils taking two subjects
Let's assume the number of pupils taking two subjects as 'x'.
Step 2: Finding the number of pupils taking three subjects
Since no student takes all three subjects, the number of pupils taking three subjects is 0.
Step 3: Finding the number of pupils taking only one subject
To find the number of pupils taking only one subject, we need to subtract the overlapping areas from the total number of pupils taking each subject.
- Number of pupils taking only Needle work = Total number of pupils taking Needle work - Number of pupils taking Needle work and Physics - Number of pupils taking Needle work and History
= 12 - x - 0 (as no student takes all three subjects)
- Number of pupils taking only Physics = Total number of pupils taking Physics - Number of pupils taking Needle work and Physics - Number of pupils taking Physics and History
= 16 - x - 0 (as no student takes all three subjects)
- Number of pupils taking only History = Total number of pupils taking History - Number of pupils taking Needle work and History - Number of pupils taking Physics and History
= 18 - x - 0 (as no student takes all three subjects)
Step 4: Finding the total number of pupils taking one subject
Since all students take at least one subject, the total number of pupils taking one subject is the sum of the number of pupils taking only Needle work, only Physics, and only History.
Total number of pupils taking one subject = Number of pupils taking only Needle work + Number of pupils taking only Physics + Number of pupils taking only History
= 12 - x + 16 - x + 18 - x
= 46 - 3x
Step 5: Finding the total number of pupils taking two subjects
Since all students take at least one subject, the total number of pupils taking two subjects is the difference between the total number of pupils (30) and the total number of pupils taking one subject.
Total number of pupils taking two subjects = Total number of pupils - Total number of pupils taking one subject
= 30 - (46 - 3x)
= 30 - 46 + 3x
= 3x - 16
Step 6: Solving the equation
We know that the total number of pupils taking two subjects is equal to the number of pupils taking two subjects (x).
3x - 16 = x
Simplifying the equation, we get:
2x = 16
x = 8
Conclusion:
Therefore, the number of pupils taking two subjects is 8. Hence, the correct answer is option C.
- Total number of pupils in the class = 30
- Number of pupils taking Needle work = 12
- Number of pupils taking Physics = 16
- Number of pupils taking History = 18
- All students take at least one subject
- No student takes all three subjects
To find:
- The number of pupils taking two subjects
Solution:
To find the number of pupils taking two subjects, we need to consider the overlapping areas of the subjects.
Step 1: Finding the number of pupils taking two subjects
Let's assume the number of pupils taking two subjects as 'x'.
Step 2: Finding the number of pupils taking three subjects
Since no student takes all three subjects, the number of pupils taking three subjects is 0.
Step 3: Finding the number of pupils taking only one subject
To find the number of pupils taking only one subject, we need to subtract the overlapping areas from the total number of pupils taking each subject.
- Number of pupils taking only Needle work = Total number of pupils taking Needle work - Number of pupils taking Needle work and Physics - Number of pupils taking Needle work and History
= 12 - x - 0 (as no student takes all three subjects)
- Number of pupils taking only Physics = Total number of pupils taking Physics - Number of pupils taking Needle work and Physics - Number of pupils taking Physics and History
= 16 - x - 0 (as no student takes all three subjects)
- Number of pupils taking only History = Total number of pupils taking History - Number of pupils taking Needle work and History - Number of pupils taking Physics and History
= 18 - x - 0 (as no student takes all three subjects)
Step 4: Finding the total number of pupils taking one subject
Since all students take at least one subject, the total number of pupils taking one subject is the sum of the number of pupils taking only Needle work, only Physics, and only History.
Total number of pupils taking one subject = Number of pupils taking only Needle work + Number of pupils taking only Physics + Number of pupils taking only History
= 12 - x + 16 - x + 18 - x
= 46 - 3x
Step 5: Finding the total number of pupils taking two subjects
Since all students take at least one subject, the total number of pupils taking two subjects is the difference between the total number of pupils (30) and the total number of pupils taking one subject.
Total number of pupils taking two subjects = Total number of pupils - Total number of pupils taking one subject
= 30 - (46 - 3x)
= 30 - 46 + 3x
= 3x - 16
Step 6: Solving the equation
We know that the total number of pupils taking two subjects is equal to the number of pupils taking two subjects (x).
3x - 16 = x
Simplifying the equation, we get:
2x = 16
x = 8
Conclusion:
Therefore, the number of pupils taking two subjects is 8. Hence, the correct answer is option C.
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In a class of 30 pupils, 12 take needle work, 16 take Physics and 18 take History. If all the 30 students take atleast one subject and no one takes all three, then the number of pupils taking 2 subjects isa)16b)6c)8d)20Correct answer is option 'A'. Can you explain this answer?
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In a class of 30 pupils, 12 take needle work, 16 take Physics and 18 take History. If all the 30 students take atleast one subject and no one takes all three, then the number of pupils taking 2 subjects isa)16b)6c)8d)20Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about In a class of 30 pupils, 12 take needle work, 16 take Physics and 18 take History. If all the 30 students take atleast one subject and no one takes all three, then the number of pupils taking 2 subjects isa)16b)6c)8d)20Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class of 30 pupils, 12 take needle work, 16 take Physics and 18 take History. If all the 30 students take atleast one subject and no one takes all three, then the number of pupils taking 2 subjects isa)16b)6c)8d)20Correct answer is option 'A'. Can you explain this answer?.
In a class of 30 pupils, 12 take needle work, 16 take Physics and 18 take History. If all the 30 students take atleast one subject and no one takes all three, then the number of pupils taking 2 subjects isa)16b)6c)8d)20Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about In a class of 30 pupils, 12 take needle work, 16 take Physics and 18 take History. If all the 30 students take atleast one subject and no one takes all three, then the number of pupils taking 2 subjects isa)16b)6c)8d)20Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class of 30 pupils, 12 take needle work, 16 take Physics and 18 take History. If all the 30 students take atleast one subject and no one takes all three, then the number of pupils taking 2 subjects isa)16b)6c)8d)20Correct answer is option 'A'. Can you explain this answer?.
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In a class of 30 pupils, 12 take needle work, 16 take Physics and 18 take History. If all the 30 students take atleast one subject and no one takes all three, then the number of pupils taking 2 subjects isa)16b)6c)8d)20Correct answer is option 'A'. Can you explain this answer?, a detailed solution for In a class of 30 pupils, 12 take needle work, 16 take Physics and 18 take History. If all the 30 students take atleast one subject and no one takes all three, then the number of pupils taking 2 subjects isa)16b)6c)8d)20Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of In a class of 30 pupils, 12 take needle work, 16 take Physics and 18 take History. If all the 30 students take atleast one subject and no one takes all three, then the number of pupils taking 2 subjects isa)16b)6c)8d)20Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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