A student finds the average of 10 two digit numbers. If the digit of one of the numbers is interchanged, the average increases by 7.2. The difference between the digits of the two digit number is

Let the original two-digit number be 10a+b (value 10a+b). When digits are interchanged, it becomes 10b+a (value 10b+a). The difference in values is (10b+a) - (10a+b) = 9(b-a) = 9×(difference of digits). This difference causes the average of 10 numbers to increase by 7.2, meaning the sum increased by 10×7.2=72. So 9×(digit difference) = 72, giving digit difference = 8. Therefore the answer is 8.