Multiple choice

While finding the average of ten two-digit odd numbers, a student by mistake took the reverse of one of the numbers, as a result of which the average went up by 2.7. What is the absolute difference between the units and the tens digit of that number?

  1. 9

  2. 2

  3. 3

  4. 4

  5. 6
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C Correct answer
Explanation

Let the number be 10x + y. Reverse is 10y + x. Difference in sum = (10y + x) - (10x + y) = 9(y - x). Average increase = 2.7, so total sum increase = 2.7 * 10 = 27. 9(y - x) = 27, so y - x = 3.

AI explanation

Let the number be 10x + y and its reverse be 10y + x. An increase in the total sum by 2.7 across 10 numbers means the total sum increased by 27. Setting the difference (10y + x) minus (10x + y) equal to 27 gives 9y minus 9x equals 27, so y minus x equals 3. The absolute difference between the unit's and ten's digit is 3.

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