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...
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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 is increased by 2 kg when...
Weight of new student =30+(2×10)=50kg
With 50kg Weight of average student increase by 2kg
The another student who joined after 50 kg student left has a weight of 50-10=40kg
The change in average weight is = 10×2=20-10 =10
as there are 10student the average change in weight =10/10 =1
Therefore option 'B' is correct.