Answer :

Let x and y be the digits in a two-digit number A = xy.


Reversing the digits, we get B = yx.


Sum of the digits in A is (10x + y).


Sum of the digits in B is (10y + x).


Sum S = A + B = (10x + y) + (10y + x).


S = 10x + x + 10y + y = 11x + 11y = 11(x + y)


The number is divisible by 11.


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