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The average weight of a class of 10 students is increased by 2 kg when one student of 30kg left and another student joined. After a few months, this new student left and another student joined whose weight was 10 less than the student who left now. What is the difference between the final and initial averages?
- a)11
- b)1
- c)111
- d)121
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The average weight of a class of 10 students is increased by 2 kg when...
Change in total weight of 10 students = difference in weight of the student who joined and the student
=> weigth of first student who left = 30 + (10×2) = 50
weight of the student who joined last = 50 – 10 = 40...
Thus change in average weight = (40 – 30)/10 = 1...
Thus change in average weight = (40 – 30)/10 = 1...
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The average weight of a class of 10 students is increased by 2 kg when...
Given:
- The average weight of a class of 10 students increased by 2 kg when one student of 30kg left and another student joined.
- After some time, this new student left and another student joined whose weight was 10 less than the student who left now.
To find: The difference between the final and initial averages.
Solution:
Let us first find the sum of weights of the initial 10 students:
Initial sum of weights = 10 × Initial average weight
Let the initial average weight be x.
Initial sum of weights = 10x
Now, the average weight increased by 2 kg when one student of 30 kg left and another student joined.
So, the sum of weights of the remaining 9 students and the new student = (10x + 2)
=> 9 × Average weight of 9 students + weight of new student = 10x + 2
=> 9(x+2) + weight of new student = 10x + 2
=> Weight of new student = x - 16
Now, the new student left and another student joined whose weight was 10 less than the student who left now.
So, the sum of weights of the remaining 9 students = (10x + 2 - x + 16 - (x - 10))
=> (9x + 8)
Final average weight = (9x + 8) / 9
The difference between the final and initial averages = Final average weight - Initial average weight
=> [(9x + 8) / 9] - x
=> (9x + 8 - 9x) / 9
=> 8/9
Therefore, the difference between the final and initial averages is 8/9, which is approximately equal to 1. Hence, the correct option is (b) 1.
- The average weight of a class of 10 students increased by 2 kg when one student of 30kg left and another student joined.
- After some time, this new student left and another student joined whose weight was 10 less than the student who left now.
To find: The difference between the final and initial averages.
Solution:
Let us first find the sum of weights of the initial 10 students:
Initial sum of weights = 10 × Initial average weight
Let the initial average weight be x.
Initial sum of weights = 10x
Now, the average weight increased by 2 kg when one student of 30 kg left and another student joined.
So, the sum of weights of the remaining 9 students and the new student = (10x + 2)
=> 9 × Average weight of 9 students + weight of new student = 10x + 2
=> 9(x+2) + weight of new student = 10x + 2
=> Weight of new student = x - 16
Now, the new student left and another student joined whose weight was 10 less than the student who left now.
So, the sum of weights of the remaining 9 students = (10x + 2 - x + 16 - (x - 10))
=> (9x + 8)
Final average weight = (9x + 8) / 9
The difference between the final and initial averages = Final average weight - Initial average weight
=> [(9x + 8) / 9] - x
=> (9x + 8 - 9x) / 9
=> 8/9
Therefore, the difference between the final and initial averages is 8/9, which is approximately equal to 1. Hence, the correct option is (b) 1.
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The average weight of a class of 10 students is increased by 2 kg when one student of 30kg left and another student joined. After a few months, this new student left and another student joined whose weight was 10 less than the student who left now. What is the difference between the final and initial averages?a)11b)1c)111d)121Correct answer is option 'B'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The average weight of a class of 10 students is increased by 2 kg when one student of 30kg left and another student joined. After a few months, this new student left and another student joined whose weight was 10 less than the student who left now. What is the difference between the final and initial averages?a)11b)1c)111d)121Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average weight of a class of 10 students is increased by 2 kg when one student of 30kg left and another student joined. After a few months, this new student left and another student joined whose weight was 10 less than the student who left now. What is the difference between the final and initial averages?a)11b)1c)111d)121Correct answer is option 'B'. Can you explain this answer?.
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