Solving for the Number

Let the original number be represented by the variable $x$. The problem states that "one-third of a number is increased by 55, the result is 77". This can be written as an algebraic equation:

$ \frac{1}{3}x + 55 = 77 $

Calculating the Original Number

To find the value of $x$, we first isolate the term with $x$ by subtracting 55 from both sides of the equation:

$ \frac{1}{3}x = 77 - 55 $

$ \frac{1}{3}x = 22 $

Next, we solve for $x$ by multiplying both sides by 3:

$ x = 22 \times 3 $

$ x = 66 $

So, the original number is 66.

Finding the Sum of Digits

The question asks for the sum of the digits of the original number (66). The digits are 6 and 6.

Sum of digits = $6 + 6 = 12$.