A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:

Let the ten's digit be x and unit's digit be y.

Then, number = 10x + y.

Number obtained by interchanging the digits = 10y + x.

 (10x + y) + (10y + x) = 11(x + y), which is divisible by 11.