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
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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