A number is increased by 20% and then decreased by 20%. Find the net i...
A number is increased by 20% and then decreased by 20%. Find the net i...
Problem:
A number is increased by 20% and then decreased by 20%. Find the net increase or decrease percent.
Solution:
To find the net increase or decrease percent, we need to understand the concept of percent increase and percent decrease.
Percent Increase:
When a number is increased by a certain percentage, the new value is calculated by adding the percentage increase to the original number.
Let's say the original number is x and the percentage increase is p.
The new value after a percent increase is calculated as:
New Value = x + (p/100) * x
= x * (1 + p/100)
Percent Decrease:
When a number is decreased by a certain percentage, the new value is calculated by subtracting the percentage decrease from the original number.
Let's say the original number is x and the percentage decrease is p.
The new value after a percent decrease is calculated as:
New Value = x - (p/100) * x
= x * (1 - p/100)
Given:
The number is increased by 20% and then decreased by 20%.
Step 1:
First, let's assume the original number as x.
Step 2:
The number is increased by 20%, which means the new value after an increase is:
New Value after increase = x * (1 + 20/100)
= x * (1 + 0.2)
= 1.2x
Step 3:
The number is then decreased by 20% from the increased value, which means the new value after a decrease is:
New Value after decrease = 1.2x * (1 - 20/100)
= 1.2x * (1 - 0.2)
= 1.2x * 0.8
= 0.96x
Step 4:
To find the net increase or decrease percent, we need to compare the final value with the original value.
The net increase or decrease percent can be calculated using the formula:
Net Increase or Decrease Percent = ((Final Value - Original Value) / Original Value) * 100
In this case,
Final Value = 0.96x
Original Value = x
Net Increase or Decrease Percent = ((0.96x - x) / x) * 100
= (-0.04x / x) * 100
= -4%
Therefore, the net increase or decrease percent is -4%.
Answer:
The net increase or decrease percent is -4%.
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