Computer Science, asked by balasubhash339, 9 months ago

The average weight of 9 boys in a class is 27 kg and the median of their weights is 30 kg The weight of the heaviest boy i 12 kg more than two times the weight of the lightest boy. The weights of all the 9 boys are integral values and the lightest and heaviest boys are exactly one each in the class. What is the maximum possible range of the weights of these 9 boys?

Pick ONE option

A) 22

B) 28

C) 30

D) 32​

Answers

Answered by amitnrw
1

Given :  The average weight of 9 boys in a class is 27 kg and the median of their weights is 30 kg The weight of the heaviest boy i 12 kg more than two times the weight of the lightest boy. The weights of all the 9 boys are integral values and the lightest and heaviest boys are exactly one each in the class.

To find : What is the maximum possible range of the weights of these 9 boys

Solution:

Weight of lightest   = a

Weight of heaviest = 2a + 12

Range = a + 12

Average weight = 27

9 students

Total Weight = 9 * 27 = 243  kg

Median Weight = 30 kg

To have maximum range a should be maximum  and to have a  maximum

( weight of 3 students between lighest & 30 kg should be minimum )

& ( weight of 3 students between 30 kg & heaviest should also be minimum )

as lighest is exactly one

hence a + 1  can be minimum weight of 3 students  

Let say weights are  to have maximum range

a   ,  a+1,  a+1 a+1  , 30  , 30 , 30 , 30    ,2a + 12

Total weight =  6a + 123

6a + 123 = 243

=> 6a  = 120

=> a = 20

2a + 12 = 52

20 , 21 , 21 , 21 , 30 , 30 , 30 , 30 , 52  are the weight of 9 students

Maximum possible range  =  52 - 20  = 32

option D is correct

32 is the maximum possible range

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