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?

Question

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?

Answer

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.

Answer

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.

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