A whole number is added to 100 and the same number is subtracted from 100. The sum of the two resulting numbers so obtained is :

The correct answer is 200.

Let's break down the problem step-by-step using logical reasoning and algebra.

Step 1: Understand the given condition
Let the unknown whole number be represented by $x$.

According to the question, two operations are performed using this number $x$:

1. The whole number is added to 100:
$\text{First number}=100+x$

2. The same whole number is subtracted from 100:
$\text{Second number}=100-x$

Step 2: Find the sum of the two resulting numbers
Now, we need to find the sum of these two resulting numbers:

$\text{Sum}=(100+x)+(100-x)$

Step 3: Simplify the expression
We can rearrange the terms by combining the constant numbers and the variable terms together:

$\text{Sum}=100+100+x-x$

Since $x-x=0$, the variable cancels out:

$\text{Sum}=100+100+0$

$\text{Sum}=200$

Conclusion:
Regardless of which whole number is chosen, the sum of the two resulting numbers will always be equal to 200.