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The average marks of the girls in a class are equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of the boys' average marks and the girls' average marks, which of the following could be the number of students in the class?
Most Upvoted Answer
The average marks of the girls in a class are equal to the number of b...
Understanding the Problem
The problem states that:
- The average marks of girls equals the number of boys (let's denote this as G).
- The average marks of boys equals the number of girls (denote this as B).
- The class average is 4 less than the average of the boys' and girls' average marks.
Formulating the Equations
From the given information, we can derive:
- Average marks of girls = G
- Average marks of boys = B
- Class average = (G + B)/2 - 4
Let the number of girls be g and the number of boys be b.
Key Relationships
- G = Total marks of girls / g
- B = Total marks of boys / b
Since G equals B, we have:
- Total marks of girls / g = Total marks of boys / b
This indicates a proportional relationship between the total marks and number of students.
Finding the Class Average
Using the information about the class average:
- Class average = (Total marks of girls + Total marks of boys) / (g + b)
This leads us to find that the class average can be expressed in terms of G and B.
Possible Values for Class Size
To find the number of students in the class (total = g + b):
- Since the average marks are integers and the relationships are based on equality, the possible class sizes must also result in integer averages.
- The possible values can be derived based on combinations of even and odd numbers of boys and girls.
Conclusion
Considering the constraints, the total class size can only be certain integers that satisfy these relationships. The most likely candidates are small integers such as 10, 12, or 14, depending on G and B being equal and the average conditions being met.
- Thus, possible class sizes could be:
- 10
- 12
- 14
This approach ensures that the average conditions hold, leading to valid integer results.
The problem states that:
- The average marks of girls equals the number of boys (let's denote this as G).
- The average marks of boys equals the number of girls (denote this as B).
- The class average is 4 less than the average of the boys' and girls' average marks.
Formulating the Equations
From the given information, we can derive:
- Average marks of girls = G
- Average marks of boys = B
- Class average = (G + B)/2 - 4
Let the number of girls be g and the number of boys be b.
Key Relationships
- G = Total marks of girls / g
- B = Total marks of boys / b
Since G equals B, we have:
- Total marks of girls / g = Total marks of boys / b
This indicates a proportional relationship between the total marks and number of students.
Finding the Class Average
Using the information about the class average:
- Class average = (Total marks of girls + Total marks of boys) / (g + b)
This leads us to find that the class average can be expressed in terms of G and B.
Possible Values for Class Size
To find the number of students in the class (total = g + b):
- Since the average marks are integers and the relationships are based on equality, the possible class sizes must also result in integer averages.
- The possible values can be derived based on combinations of even and odd numbers of boys and girls.
Conclusion
Considering the constraints, the total class size can only be certain integers that satisfy these relationships. The most likely candidates are small integers such as 10, 12, or 14, depending on G and B being equal and the average conditions being met.
- Thus, possible class sizes could be:
- 10
- 12
- 14
This approach ensures that the average conditions hold, leading to valid integer results.
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The average marks of the girls in a class are equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of the boys' average marks and the girls' average marks, which of the following could be the number of students in the class?
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The average marks of the girls in a class are equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of the boys' average marks and the girls' average marks, which of the following could be the number of students in the class? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The average marks of the girls in a class are equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of the boys' average marks and the girls' average marks, which of the following could be the number of students in the class? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average marks of the girls in a class are equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of the boys' average marks and the girls' average marks, which of the following could be the number of students in the class?.
The average marks of the girls in a class are equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of the boys' average marks and the girls' average marks, which of the following could be the number of students in the class? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The average marks of the girls in a class are equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of the boys' average marks and the girls' average marks, which of the following could be the number of students in the class? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average marks of the girls in a class are equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of the boys' average marks and the girls' average marks, which of the following could be the number of students in the class?.
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The average marks of the girls in a class are equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of the boys' average marks and the girls' average marks, which of the following could be the number of students in the class?, a detailed solution for The average marks of the girls in a class are equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of the boys' average marks and the girls' average marks, which of the following could be the number of students in the class? has been provided alongside types of The average marks of the girls in a class are equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of the boys' average marks and the girls' average marks, which of the following could be the number of students in the class? theory, EduRev gives you an
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