Question

Question No. 17
The arithmetic mean of x and y is 30 and that of y and z is 25. It is known that x, y, z are positive integers and x >y> z. What is the difference between the ranges (i.e., the
difference between the maximum and the minimum possible value) of x and z?​

Answer 1

Given :  The arithmetic mean of x and y is 30 and that of y and z is 25. It is known that x, y, z are positive integers and x >y> z.

To Find : the difference between the maximum and the minimum possible value) of x and z

Solution:

The arithmetic mean of x and y is 30

=> (x + y)/2 = 30

=> x + y = 60

x , y are positive integers and x  > y

so maximum  value of  is  x is 59 when y = 1

minimum value of x is 31 when  y is 29

=>  1 ≤ y  ≤ 29

The arithmetic mean of z and y is 25

=> (z + y)/2 = 25

=> z + y = 50

z , y are positive integers and y  > z

so maximum  value of  is  z is 24 when y = 26

minimum value of z is  1 when  y is  49

=>  26 ≤ y  ≤ 49

1 ≤ y  ≤ 29

26 ≤ y  ≤ 49

from both

26  ≤  y  ≤ 29

y = 26  => x  = 34     ,   z = 24            

y = 29 =>  x  =  31     ,   z  =  21

Maximum possible value x = 34

minimum possible value of z  = 21

34 - 21  = 13

difference between the maximum and the minimum possible value) of x and z is 13

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