A student finds the average of ten 2 digit numbers. While copying numbers, by mistake, he writes one number with its digits interchanged. As a result his answer is 2.7 less than the correct answer. The difference of the digit of the number, in which he made mistake is:

A student finds the average of ten 2 digit numbers.

While copying numbers, by mistake, he writes one number with its digits interchanged.

As a result his answer is 2.7 less than the correct answer.

Let the digits of the number be 'ab'
The number = 10a + b
After interchanging the digit, the number becomes 10b + a

The difference between these two numbers is: (10a + b) − (10b + a)

= 9a − 9b

= 9(a − b)

The difference in average after interchanging the digits = 2.7
As there are 10 numbers,
The difference between the numbers will be = 2.7 × 10 = 27
 Now, 

9(a − b) = 27

(a - b ) = 3

So, the difference between the digits is 3.

Thus, the correct answer is (c).