In this question, we are given a number consisting of two digits. We need to determine the number by which we can divide the original number after interchanging the digits and adding it to the original number for it to be divisible.

Let`s consider an example using a two-digit number xy, where x represents the tens digit and y represents the units digit.

When the digits interchange places, the new number becomes yx.

Now, let`s add this new number (yx) to the original number (xy):

xy + yx = 10x + y + 10y + x = 11x + 11y = 11(x + y)

To check if the resulting number is divisible by a specific number, we need to check if (x + y) is divisible by that number. In this case, the resulting number is divisible by 11, as it is a multiple of 11.

Therefore, the correct answer is option 2: 11.

Alert - correct answer should be 11