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Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?
A 40.18 kgs
B 40.56 kgs
C 40.67 kgs
D 40.49 kgs
E 40.78 Kgs
Are You Up For the Challenge: 700 Level Questions
A 40.18 kgs
B 40.56 kgs
C 40.67 kgs
D 40.49 kgs
E 40.78 Kgs
Are You Up For the Challenge: 700 Level Questions
Bunuel
Use the method of deviations discussed here: https://anaprep.com/arithmetic-usefulne ... eviations/
Assume that all the 40 students have weight of 40 kgs each.
Consider m = 1, n = 49. We have excess of 9 to be distributed among 41 students. So average will increase by 9/41
If m = 2, n = 48, we have excess of 16 to be distributed among 42 students. So average will increase by 16/42.
...
If m = 4, n = 46, we have excess of 24 to be distributed among 44 students. So average will increase by 24/44.
If m = 5, n = 45, we have excess of 25 to be distributed among 45 students. So average will increase by 25/45 (a little bit more than 0.5 kgs)
If m = 6, n = 44, we have excess of 24 to be distributed among 46 students. So average will increase by 24/46 (the increase in average is reducing now since 24/46 is less than 24/44))
...
So the average will increase at most by a bit more than 0.5 kgs. Hence answer must be (B).
General Discussion
As we have to find out maximum average weight the number of new student should be minimum.
Let, the the average weight n=49 so m=1as m+n=50
Now,total weight =(40*40)+49=1649
And number of students =40+1=41
So maximum average weight =1649/41=40.2=~40.18kg
Ans A
Posted from my mobile device
Let, the the average weight n=49 so m=1as m+n=50
Now,total weight =(40*40)+49=1649
And number of students =40+1=41
So maximum average weight =1649/41=40.2=~40.18kg
Ans A
Posted from my mobile device
