For a set of ten numbers, removing the largest number decreases the average by 1. Removing the smallest number increases the average by 2. What is the positive difference between the largest and the smallest of these ten numbers

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