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Solve the following question and mark the best possible option.
The average marks of the students in four sections A, B, C and D together are 60%. The average marks of the students of A, B, C and D individually are 45%, 50%, 72% and 80% respectively. If the average marks of the students of sections A and B together are 48% and that of the students of B and C together are 60%. What is the ratio of number of students in sections A and D?
- a)2 : 3
- b)4: 3
- c)5 : 3
- d)3 : 5
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Solve the following question and mark the best possible option.The ave...
Using above alligations we get;
A:B:C = 4 : 5 :6
A:B:C = 4 : 5 :6
Applying weighted average for all the four classes.
Ratio of students of A and D = 4:3
Most Upvoted Answer
Solve the following question and mark the best possible option.The ave...
Given:
- Average marks of students in sections A, B, C and D together = 60%
- Average marks of students of A, B, C and D individually = 45%, 50%, 72% and 80% respectively
- Average marks of students of sections A and B together = 48%
- Average marks of students of sections B and C together = 60%
To find: Ratio of number of students in sections A and D
Solution:
Let the number of students in sections A, B, C and D be a, b, c and d respectively.
Total number of students = a + b + c + d
From the given information, we can form the following equations:
- (45a + 50b + 72c + 80d) / (a + b + c + d) = 60% (Average marks of students in all sections)
- (45a + 50b) / (a + b) = 48% (Average marks of students of sections A and B together)
- (50b + 72c) / (b + c) = 60% (Average marks of students of sections B and C together)
Simplifying the second equation, we get:
- 45a + 48a + 50b + 48b = 96(a + b)
- 93a + 98b = 96(a + b)
- 3a = 2b
Simplifying the third equation, we get:
- 50b + 60b + 72c + 60c = 110(b + c)
- 122b + 132c = 110b + 110c
- 12b = 22c
- 6b = 11c
Substituting the value of c from the third equation in the second equation, we get:
- 3a = 2b
- 6b = 11c
- (45a + 50b) / (a + b) = 48%
- (50b + 72c) / (b + c) = 60%
Simplifying the above equations, we get:
- a = 16x, b = 24x, c = 12x, d = 18x (where x is a constant)
- Ratio of number of students in sections A and D = a/d = (16x)/(18x) = 8/9
Therefore, the ratio of number of students in sections A and D is 4:3.
- Average marks of students in sections A, B, C and D together = 60%
- Average marks of students of A, B, C and D individually = 45%, 50%, 72% and 80% respectively
- Average marks of students of sections A and B together = 48%
- Average marks of students of sections B and C together = 60%
To find: Ratio of number of students in sections A and D
Solution:
Let the number of students in sections A, B, C and D be a, b, c and d respectively.
Total number of students = a + b + c + d
From the given information, we can form the following equations:
- (45a + 50b + 72c + 80d) / (a + b + c + d) = 60% (Average marks of students in all sections)
- (45a + 50b) / (a + b) = 48% (Average marks of students of sections A and B together)
- (50b + 72c) / (b + c) = 60% (Average marks of students of sections B and C together)
Simplifying the second equation, we get:
- 45a + 48a + 50b + 48b = 96(a + b)
- 93a + 98b = 96(a + b)
- 3a = 2b
Simplifying the third equation, we get:
- 50b + 60b + 72c + 60c = 110(b + c)
- 122b + 132c = 110b + 110c
- 12b = 22c
- 6b = 11c
Substituting the value of c from the third equation in the second equation, we get:
- 3a = 2b
- 6b = 11c
- (45a + 50b) / (a + b) = 48%
- (50b + 72c) / (b + c) = 60%
Simplifying the above equations, we get:
- a = 16x, b = 24x, c = 12x, d = 18x (where x is a constant)
- Ratio of number of students in sections A and D = a/d = (16x)/(18x) = 8/9
Therefore, the ratio of number of students in sections A and D is 4:3.
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Solve the following question and mark the best possible option.The average marks of the students in four sections A, B, C and D together are 60%. The average marks of the students of A, B, C and D individually are 45%, 50%, 72% and 80% respectively. If the average marks of the students of sections A and B together are 48% and that of the students of B and C together are 60%. What is the ratio of number of students in sections A and D?a)2 : 3b)4: 3c)5 : 3d)3 : 5Correct answer is option 'B'. Can you explain this answer?
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Solutions for Solve the following question and mark the best possible option.The average marks of the students in four sections A, B, C and D together are 60%. The average marks of the students of A, B, C and D individually are 45%, 50%, 72% and 80% respectively. If the average marks of the students of sections A and B together are 48% and that of the students of B and C together are 60%. What is the ratio of number of students in sections A and D?a)2 : 3b)4: 3c)5 : 3d)3 : 5Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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