Vedic Math fun with Digit Sums

What is Digit Sum:
The sum of all the digits in a number is Digit Sum.
e.g. The digit sum of 125 is 1 + 2 + 5 = 8
The digit sum of 1357 is 1 + 3 + 5 + 7 = 16

Some fun with Digit Sums:
Let's add a 2 digit number with the number generated by reversing its digits.
For Example, for 28, we have to add 28 + 82 =  110
Let's see few more examples:
16 + 61 = 77
13 + 31 = 44
38 + 83 = 121
27 + 72 = 99

The result is in a pattern. You can see, all the numbers are divisible by 11.

Let's derive an equation out of the above calculation.

We have a number xy. The number with reversed digits will be yx.

So, xy + yx = 10x + y + 10y + x = 11x + 11y = 11 * (x + y)

So the conclusion is "When we add a 2 digit number with another number resulting from reversing the digits, the result will be 11 times their Digit Sum".

To verify this, let's take above examples again.

28 + 82 =  110 = 11 * (2 + 8)
16 + 61 = 77 = 11 * (1 + 6)