The average of nine 2 digit numbers is decreased by 6 when the digits of one of the 2 digit numbers is interchanged. Find the difference between the digits of that number.

Let the two digits of the number are $$a$$ and $$b$$

Two digit number = $$10a+b$$

Two digit number when digits are interchanged = $$10b+a$$

According to the problem,

$$\frac{\text{Sum of remaining 8 numbers}+10a+b}{9}-6=\frac{\text{Sum of remaining 8 numbers}+10b+a}{9}$$

$$\Rightarrow$$  Sum of remaining 8 numbers $$+10a+b-54=$$ Sum of remaining 8 numbers $$+10b+a$$

$$\Rightarrow$$  $$9a-9b=54$$

$$\Rightarrow$$  $$9\left(a-b\right)=54$$

$$\Rightarrow$$  $$a-b=6$$

$$\therefore\ $$Difference between digits of the number = 6

Hence, the correct answer is Option A