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 :

A. 4

B. 3

C. 2

D. 5

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Solution(By Apex Team)

According to the question, Let as consider by mistake he writes 10th number with its digits interchanged $\begin{array}{l}\therefore\left[\Large\frac{10x+y-(10y+x)}{10}\right]=3.6\end{array}$ ∴ In these remaining nine numbers are same and they cancel out $\begin{array}{l}\Rightarrow\left[\Large\frac{10x+y-(10y+x)}{10}\right]=3.6\\ \Rightarrow9x-9y=36\\ \Rightarrow x-y=4\end{array}$