Finding the Original Number

Let the original number be represented by '$x$'.

According to the question, when one-third of the number is increased by 37, the result is 51. This can be written as the equation:

$ \frac{1}{3}x + 37 = 51 $

Solving the Equation

To find the value of '$x$', we first isolate the term with '$x$':

$ \frac{1}{3}x = 51 - 37 $

$ \frac{1}{3}x = 14 $

Now, multiply both sides by 3 to find the value of '$x$':

$ x = 14 \times 3 $

$ x = 42 $

So, the original number is 42.

Calculating the Sum of Digits

The question asks for the sum of the digits of the original number (42).

Sum of digits = $4 + 2 = 6$.

Final Answer Check

Verify the result: One-third of 42 is $ \frac{42}{3} = 14 $. Increasing this by 37 gives $ 14 + 37 = 51 $. This matches the condition given in the problem.