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Consider a class of 40 students whose average weight is 40 kgs. m new

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Bunuel
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Consider a class of 40 students whose average weight is 40 kgs. m new [#permalink] Consider a class of 40 students whose average weight is 40 kgs. m new   06 Dec 2021, 05:15
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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


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Consider a class of 40 students whose average weight is 40 kgs. m new [#permalink] Consider a class of 40 students whose average weight is 40 kgs. m new   Updated on: 18 Dec 2021, 17:57
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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

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Originally posted by Carpenter on 18 Dec 2021, 17:33.
Last edited by Carpenter on 18 Dec 2021, 17:57, edited 1 time in total.
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Consider a class of 40 students whose average weight is 40 kgs. m new [#permalink] Consider a class of 40 students whose average weight is 40 kgs. m new   Updated on: 23 Aug 2023, 00:27
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Bunuel
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


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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).

Originally posted by KarishmaB on 22 Dec 2021, 02:54.
Last edited by KarishmaB on 23 Aug 2023, 00:27, edited 2 times in total.
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Re: Consider a class of 40 students whose average weight is 40 kgs. m new [#permalink] Consider a class of 40 students whose average weight is 40 kgs. m new   22 Dec 2021, 10:01
KarishmaB

Could you please confirm whether denominator should be 41 instead of 49?
Consider m = 1, n = 49. We have excess of 9 to be distributed among 41 students. So average will increase by 9/49
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Re: Consider a class of 40 students whose average weight is 40 kgs. m new [#permalink] Consider a class of 40 students whose average weight is 40 kgs. m new   22 Dec 2021, 20:03
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rsrighosh
KarishmaB

Could you please confirm whether denominator should be 41 instead of 49?
Consider m = 1, n = 49. We have excess of 9 to be distributed among 41 students. So average will increase by 9/49

Yes. Edited. Thanks.
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Re: Consider a class of 40 students whose average weight is 40 kgs. m new [#permalink] Consider a class of 40 students whose average weight is 40 kgs. m new   22 Sep 2024, 10:22
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