Solution:

The number is 54, simply because
54 = 6 (5 + 4).

How does one find this number?

Let t be the digit in the tens place and u be the digit in the units place. Then, the number is 10 t + u, and the sum of its digits is t + u. The following equation can be readily written:

10 t + u = 6 t + 6 u or
4 t = 5 u.

Thus, t / u = 5 / 4. Since t and u are digits, t must be 5 and u must be 4.

Food for thought:

Is the assumption of a 2-digit number a valid one?