Percentage Reduction Formula
The percentage reduction is used to compare the decay/reduction in two quantities with different initial values. For example, consider the following two businesses. In the table below, we can see that both businesses reduced by $5,000. Does this mean that they are decaying at the same rate? No, because the decay has to be compared with the initial value. We use the percentage reduction formula for this.
Initial Investment  Final Value of the Business  

Business1  $15,000  $10,000 
Business2  $35,000  $30,000 
What Is the Percentage reduction Formula?
The percentage reduction formula is the ratio of the reduction in the quantity to its initial value multiplied by 100. Since the percentage has to be a positive quantity, we take the absolute value of the initial value. i.e.,
From the previous example,
Reduction in business1 = 15000  10000 = $5000.
Reduction in business2 = 35000  30000 = $5000.
Let us calculate the percentage reduction in each of business1 and business2.
Percentage reduction of business1 = (5000 / 15000) * 100 = 33.33%
Percentage reduction of business2 = (5000 / 35000) * 100 = 14.28%
It means business1 has a more decay rate.
Solved Examples Using Percentage Reduction Formula

Example 1: The price of Ken's toy car was reduced from $20 to $15. Find its percentage reduction. Solve this by using the percentage reduction formula.
Solution:
To find:' Percentage reduction in the price of the toy car.
The initial value of the car = $20.
The final value of the car = $15.
The reduction in the value = 20  15 = $5.
Using the percentage reduction formula,
Percentage reduction = (Reduction in the quantity / Initial value of the quantity) * 100
= (5 / 20) * 100
= (5 / 20) * 100
= 25%
Answer: Percentage reduction in the toy car = 25%.

Example 2: The height of a tower was reduced from 50 ft to 30 ft. Find the percentage reduction in the height of the tower. Solve this by using the percentage reduction formula.
Solution:
To find: Percentage reduction in the height of the tower.
The initial height of the tower = 50 ft.
The final height of the tower = 30 ft.
The reduction in the height = 50  30 = 20 ft.
Using the percentage reduction formula,
Percentage reduction = (Reduction in the height / Initial height of the quantity) * 100
= (20 / 50) * 100
= (20 / 50) * 100
= 40%
Answer: Percentage reduction in the height of the tower = 40%