Introduction:

In this problem, we need to show that when a number is increased by 10% and then the increased number is decreased by 10%, the net decrease is 1%. Let's break down the problem step by step to understand the concept and how it leads to a net decrease of 1%.

Step 1: Increasing the number by 10%:

Let's consider the original number as "x". When the number is increased by 10%, the new number becomes x + (10/100)x, which can be simplified as 1.1x.

Step 2: Decreasing the increased number by 10%:

Now, we need to decrease the increased number (1.1x) by 10%. This can be calculated as (1.1x) - (10/100)(1.1x), which simplifies to 1.1x - (0.11x), and further simplifies to 0.99x.

Step 3: Calculating the net decrease:

To find the net decrease, we need to compare the final number (0.99x) with the original number (x). The difference between the final number and the original number can be calculated as (0.99x - x).

Step 4: Expressing the net decrease as a percentage:

To express the net decrease as a percentage, we divide the difference obtained in step 3 by the original number and multiply by 100. So, the net decrease percentage can be calculated as ((0.99x - x)/x) * 100.

Simplifying the expression:

Let's simplify the expression ((0.99x - x)/x) * 100 to understand the net decrease percentage better.

((0.99x - x)/x) * 100 can be written as ((0.99 - 1)/1) * 100x, which further simplifies to (-0.01) * 100x.

Therefore, the net decrease percentage is -1%, which means there is a 1% decrease in the final number compared to the original number.

Conclusion:

In conclusion, when a number is increased by 10% and then the increased number is decreased by 10%, the net decrease is 1%. This can be mathematically proven by calculating the difference between the final number and the original number, and expressing it as a percentage.