Answer:
27
Step-by-step explanation:
Let the largest number=a
Let the smallest number=b
If the total of all the 10 numbers =y
Average of all the 10 numbers=x
Then: y/10=x
Now, removing the largest number decreases the average by 1
(y-a)/9=x-1
y-a=9(x-1)
y-a=9x-9
Largest number, a=y-9x+9
Also, removing the smallest number increases the average by 2.
(y-b)/9=x+2
y-b=9(x+1)
y-b=9x+18
Smallest number, b=y-9x-18
The positive difference between the largest and the smallest
a-b=(y-9x+9)-(y-9x-18)
=y-9x+9-y+9x+18
=y-y-9x+9x+9+18
=27
