A number is increased by 20 percent and then decreased by 20 percent f...
Introduction:
To find the net increase or decrease percent, we need to understand the concept of percentage increase and decrease and how they affect a number. Let's break down the problem step by step.
Given:
A number is increased by 20 percent and then decreased by 20 percent.
Step 1: Increase by 20 percent:
When a number is increased by a certain percentage, we multiply the number by 1 plus the percentage increase in decimal form. In this case, the number is increased by 20 percent, which is equivalent to multiplying the number by 1 + 0.2.
Step 2: Decrease by 20 percent:
When a number is decreased by a certain percentage, we multiply the number by 1 minus the percentage decrease in decimal form. In this case, the number is decreased by 20 percent, which is equivalent to multiplying the number by 1 - 0.2.
Calculating the net increase or decrease percent:
To calculate the net increase or decrease percent, we need to find the difference between the final number and the original number and express it as a percentage of the original number.
Step 3: Find the final number:
Let's assume the original number is x. After the initial increase by 20 percent, the number becomes x * (1 + 0.2) = 1.2x. After the subsequent decrease by 20 percent, the number becomes (1.2x) * (1 - 0.2) = 0.96x.
Step 4: Calculate the difference:
The difference between the final number and the original number is 0.96x - x = -0.04x.
Step 5: Calculate the net increase or decrease percent:
To express the difference as a percentage of the original number, we divide the difference by the original number and multiply by 100. In this case, the net increase or decrease percent is (-0.04x / x) * 100 = -4%.
Conclusion:
The net increase or decrease percent after increasing a number by 20 percent and then decreasing it by 20 percent is -4%. This means there is a net decrease of 4 percent.
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