Algebraic Equation Setup

Let the original number be represented by the variable $x$. The problem states that "one-third of a number is increased by 10, the result is 65". We can translate this into an algebraic equation:

$ \frac{x}{3} + 10 = 65 $

Solving for the Number

To find the original number ($x$), we first isolate the term with $x$ by subtracting 10 from both sides of the equation:

$ \frac{x}{3} = 65 - 10 $

$ \frac{x}{3} = 55 $

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

$ x = 55 \times 3 $

$ x = 165 $

So, the original number is 165.

Calculating the Sum of Digits

The question asks for the sum of the digits of the original number, which is 165. The digits are 1, 6, and 5.

Sum of digits = $1 + 6 + 5$

Sum of digits = $12$

Final Answer

The sum of the digits of the original number is 12.