QueSCIUIT 9.
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 is 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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Answer:
d is correct 32 will be the answer
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