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There are three classes A, B and C with a certain number of students in each of them.In a given test, the performance of the students of various classes is measured. It is found that the average mark of Class A students is 80. The average mark of Class B students is 71. The average mark of Class C students is 82. If the average mark of Class A and B students combined is 75, and the average mark of Class B and C students is 77, then the average mark of the three classes is?
  • a)
    77.8
  • b)
    67.5
  • c)
    96
  • d)
    84
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
There are three classes A, B and C with a certain number of students i...

So, the ratio of students of A to B is 4 : 5
And the ratio of students of B to C is 5 : 6
Now, A : B : C = 4 : 5 : 6 
So, average of all the classes 
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Most Upvoted Answer
There are three classes A, B and C with a certain number of students i...
Given information:
- Average mark of Class A students = 80
- Average mark of Class B students = 71
- Average mark of Class C students = 82
- Average mark of Class A and B students combined = 75
- Average mark of Class B and C students combined = 77

To find: Average mark of all three classes combined

Solution:
1. Let's start by finding the total number of students in all three classes combined.
- Let the number of students in Class A be a
- Let the number of students in Class B be b
- Let the number of students in Class C be c
- Then, the total number of students = a + b + c

2. Next, let's find the total marks obtained by all the students in each class.
- Total marks obtained by Class A students = 80a
- Total marks obtained by Class B students = 71b
- Total marks obtained by Class C students = 82c

3. Using the given information, we can form two equations:
- (Total marks obtained by Class A and B students) / (Total number of Class A and B students) = 75
=> (80a + 71b) / (a + b) = 75
=> 80a + 71b = 75a + 75b
=> 5a = 4b
- (Total marks obtained by Class B and C students) / (Total number of Class B and C students) = 77
=> (71b + 82c) / (b + c) = 77
=> 71b + 82c = 77b + 77c
=> 11b = 5c

4. Using the above equations, we can find the values of a, b, and c:
- From equation 1: b = (5/4)a
- Substituting in equation 2: c = (11/5)b = (11/5) * (5/4)a = (11/4)a
- Total number of students = a + b + c = a + (5/4)a + (11/4)a = (17/4)a
- Simplifying: a = (4/17) * (Total number of students)
- Substituting in equation 1: b = (5/4)a = (5/4) * (4/17) * (Total number of students) = (5/17) * (Total number of students)
- Substituting in equation 2: c = (11/4)a = (11/4) * (4/17) * (Total number of students) = (11/17) * (Total number of students)

5. Now, we can find the total marks obtained by all the students in all three classes combined:
- Total marks obtained = 80a + 71b + 82c
- Substituting the values of a, b, and c from step 4:
Total marks obtained = 80 * (4/17) * (Total number of students) + 71 * (5/17) * (Total number of students) + 82 * (11/17) * (Total number of students)
Total marks obtained = (440/17)
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There are three classes A, B and C with a certain number of students in each of them.In a given test, the performance of the students of various classes is measured. It is found that the average mark of Class A students is 80. The average mark of Class B students is 71. The average mark of Class C students is 82. If the average mark of Class A and B students combined is 75, and the average mark of Class B and C students is 77, then the average mark of the three classes is?a)77.8b)67.5c)96d)84Correct answer is option 'A'. Can you explain this answer?
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There are three classes A, B and C with a certain number of students in each of them.In a given test, the performance of the students of various classes is measured. It is found that the average mark of Class A students is 80. The average mark of Class B students is 71. The average mark of Class C students is 82. If the average mark of Class A and B students combined is 75, and the average mark of Class B and C students is 77, then the average mark of the three classes is?a)77.8b)67.5c)96d)84Correct answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about There are three classes A, B and C with a certain number of students in each of them.In a given test, the performance of the students of various classes is measured. It is found that the average mark of Class A students is 80. The average mark of Class B students is 71. The average mark of Class C students is 82. If the average mark of Class A and B students combined is 75, and the average mark of Class B and C students is 77, then the average mark of the three classes is?a)77.8b)67.5c)96d)84Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are three classes A, B and C with a certain number of students in each of them.In a given test, the performance of the students of various classes is measured. It is found that the average mark of Class A students is 80. The average mark of Class B students is 71. The average mark of Class C students is 82. If the average mark of Class A and B students combined is 75, and the average mark of Class B and C students is 77, then the average mark of the three classes is?a)77.8b)67.5c)96d)84Correct answer is option 'A'. Can you explain this answer?.
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