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

average =$$\frac{SumofElements}{NumberofElements}$$

Let the average of 10 two digit number be y

Sum of 10 two digit number = 10 × y

Now if digits of 1 number is interchanged , new average = y+3.6

This increment is because of change in digits of 1 two digit number .

Sum of 10 numbers after interchanging digits = 10y + 36

Difference between the two cases = 9 × difference between digits of 1 two digit number whose digits have been interchanged and the unit digit of this number is greater than tens digit = 9 (b-a)

Where " ab " is the two digit number whose digits have been interchanged.

9 (b-a) = 36

Hence , (b-a ) = 4