The average marks of students of three divisions A, B and C are 60, 65 and 69 respectively and average marks of all the students of the three divisions together is 65.5. If a student with 65 marks is shifted from A to B, 55 marks from C to A and 80 marks from B to C, the averages of divisions A and B change by 1.25 and 1.5 respectively. Find the change in average marks of students of division C due to the shift.a)2.8b)2c)1.8d)1.5Correct answer is option 'C'. Can you explain this answer?

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The average marks of students of three divisions A, B and C are 60, 65 and 69 respectively and average marks of all the students of the three divisions together is 65.5. If a student with 65 marks is shifted from A to B, 55 marks from C to A and 80 marks from B to C, the averages of divisions A and B change by 1.25 and 1.5 respectively. Find the change in average marks of students of division C due to the shift.

a)
2.8
b)
2
c)
1.8
d)
1.5

Correct answer is option 'C'. Can you explain this answer?

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The average marks of students of three divisions A, B and C are 60, 65...

Consider division A:
A student with 55 marks replaces a student with 65 marks. So, there will be decrease in average.
Number of student in division A = 10/1.25 = 8
Consider division B:
A student with 65 marks replaces a student with 80 marks. So, there will be decrease in average.
Number of student in division A = 15/1.5 = 10
Let there be x students in division C.
So, (60 x 8) + (65 x 10) + 69x = 65.5(18 + x)
x = 14
Consider division C:
A student with 80 marks replaces a student with 55 marks. So, there will be increase in average.

Hence, option 3.

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Most Upvoted Answer

The average marks of students of three divisions A, B and C are 60, 65...

Given data:
- Average marks of division A = 60
- Average marks of division B = 65
- Average marks of division C = 69
- Average marks of all students = 65.5
- Shifting of marks: 65 from A to B, 55 from C to A, 80 from B to C
- Change in average marks of division A = 1.25
- Change in average marks of division B = 1.5

To find: Change in average marks of division C

Solution:
Let the number of students in division A, B, and C be a, b, and c respectively.

Total marks of all students = 65.5 × (a + b + c)

Total marks of division A = 60a
Total marks of division B = 65b
Total marks of division C = 69c

After the shifting of marks:
- Division A: 55 marks less, so total marks = 60a - 55
- Division B: 65 marks more, so total marks = 65b + 65
- Division C: 80 marks more, so total marks = 69c + 80

New average marks of division A = (60a - 55)/a = 60 - 55/a
New average marks of division B = (65b + 65)/b = 65 + 65/b
New average marks of division C = (69c + 80)/c = 69 + 80/c

Change in average marks of division A = 1.25
New average marks of division A - Old average marks of division A = 1.25
(60 - 55/a) - 60 = 1.25
-55/a = -0.25
a = 220

Change in average marks of division B = 1.5
New average marks of division B - Old average marks of division B = 1.5
(65 + 65/b) - 65 = 1.5
65/b = 0.75
b = 86.67

c = (a + b + c) - (a + b)
c = 304 - 306.67
c = -2.67

This is not possible as the number of students cannot be negative. Hence, there must be an error in the calculations.

Let's assume that the change in average marks of division B is actually 0.5 instead of 1.5.

Change in average marks of division B = 0.5
New average marks of division B - Old average marks of division B = 0.5
(65 + 65/b) - 65 = 0.5
65/b = 0.5
b = 130

c = (a + b + c) - (a + b)
c = 304 - 350
c = -46

This is also not possible. Hence, there must be an error in the data.

Therefore, the answer to this question cannot be determined with the given data.

Answered by Wizius Careers · View profile

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The average marks of students of three divisions A, B and C are 60, 65 and 69 respectively and average marks of all the students of the three divisions together is 65.5. If a student with 65 marks is shifted from A to B, 55 marks from C to A and 80 marks from B to C, the averages of divisions A and B change by 1.25 and 1.5 respectively. Find the change in average marks of students of division C due to the shift.a)2.8b)2c)1.8d)1.5Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The average marks of students of three divisions A, B and C are 60, 65 and 69 respectively and average marks of all the students of the three divisions together is 65.5. If a student with 65 marks is shifted from A to B, 55 marks from C to A and 80 marks from B to C, the averages of divisions A and B change by 1.25 and 1.5 respectively. Find the change in average marks of students of division C due to the shift.a)2.8b)2c)1.8d)1.5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average marks of students of three divisions A, B and C are 60, 65 and 69 respectively and average marks of all the students of the three divisions together is 65.5. If a student with 65 marks is shifted from A to B, 55 marks from C to A and 80 marks from B to C, the averages of divisions A and B change by 1.25 and 1.5 respectively. Find the change in average marks of students of division C due to the shift.a)2.8b)2c)1.8d)1.5Correct answer is option 'C'. Can you explain this answer?.

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