A student finds the average of 10, 2 digits numbers. If the digits of one of the numbers interchanged, the average increases by 3.6. The difference between the digits of the 2 digits number is :

Answer: Option A

According to the question,
Let as consider by mistake he writes 10th number with its digits interchanged
∴ $$\frac{10x+y-\left(10y+x\right)}{10}=3.6$$
∴ In these remaining nine numbers are same and they cancel out
$$\begin{array}{rl}& \Rightarrow \frac{10x+y-\left(10y+x\right)}{10}=3.6\\ & \Rightarrow 9x-9y=36\\ & \Rightarrow x-y=4\end{array}$$