Let the number of times, the tens, and the units digits be, N, T and U, respectively

Then we have: 10T + U + 10U + T = N(T + U)

11T + 11U = N(T + U)

11(T + U) = N(T + U)

11 = N



The sum of a two digit number and the number obtained by inter changing the digits is  times the sum of their digits. 

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