If a workers salary is increased by 10 % and then reduced by 10%, state whether he loses or
gains, and by what percentage?

When a worker's salary is increased by 10% and then reduced by 10%, the worker ends up **losing** money. Here's the reasoning:

### Let's assume the initial salary is 100 units.

1. **First increase of 10%**:
   \[
   100 + 10\% \text{ of } 100 = 100 + 10 = 110
   \]
   After the increase, the new salary becomes 110 units.

2. **Now, reduce this new salary by 10%**:
   \[
   10\% \text{ of } 110 = 11
   \]
   After the reduction, the new salary becomes:
   \[
   110 - 11 = 99
   \]

The final salary is **99 units**, which means the worker has lost 1 unit compared to the original salary of 100 units. This is a **1% loss**.

### Conclusion:
- The worker loses **1%** of their original salary.

Would you like more details on how this happens or have any other questions?

Here are 5 related questions:
1. How do repeated percentage changes affect overall value?
2. What if the increase and decrease were different percentages (e.g., 20% increase and 10% decrease)?
3. Can we apply this principle to other contexts, such as investments?
4. What would happen if the salary was reduced first and then increased by the same percentage?
5. How do we calculate percentage changes in reverse (e.g., what percentage increase recovers a 10% loss)?

**Tip**: When working with percentages, increases and decreases are applied to different base values, which can lead to unexpected results like a net loss!

If a worker's salary is increased by 10% and then reduced by 10%, state whether he loses or gains, and by what percentage?

Discover how a worker's salary is affected by a 10% increase followed by a 10% decrease. Learn why this results in a 1% net loss, with step-by-step calculations. Perfect for students in Grades 6-8 learning about percentage changes.

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