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 :

Question

Accepted Answer

To solve the problem, let's break down the steps involved:

1. **Understanding the Problem:**
   - A whole number, let's call it $ x $, is added to 100. This gives us the expression $ 100 + x $.
   - The same number $ x $ is subtracted from 100. This gives us the expression $ 100 - x $.

2. **Calculating the Sum:**
   - We need to find the sum of the two resulting numbers: $ (100 + x) + (100 - x) $.

3. **Simplifying the Expression:**
   - When we add the two expressions, the $ x $ terms cancel each other out:
     $$
     (100 + x) + (100 - x) = 100 + x + 100 - x = 200
     $$

4. **Conclusion:**
   - The sum of the two resulting numbers is 200, which corresponds to Option 1.

**Explanation of Why Other Options Are Incorrect:**

- **Option 2 (0):** This option would imply that the sum of the two expressions results in zero, which is not possible since both expressions are positive and their sum is clearly 200.

- **Option 3 (50):** This option suggests that the sum of the two expressions is 50. However, as shown in the calculation, the sum is 200, not 50.

- **Option 4 (100):** This option implies that the sum of the two expressions is 100. Again, the calculation clearly shows that the sum is 200, not 100.

Therefore, based on the logical and mathematical reasoning provided, Option 1 is indeed the correct answer.