Percent Decrease Formula
The percent decrease formula for any item is given by,
Percent Decrease = \( \left ( \frac{\text{Decreased Value}}{\text{Original Value}} \right )~\times~100\)
Here, the decreased value can be obtained by subtracting the new value from the original value. We can write it as,
Decreased value = Original value – New value
Solved Examples
Example 1: A hairbrush costing $45 is sold at $30. Find the percent decrease of the price of the hairbrush.
Answer: Here, new value = $30, and, original value = $45
By using the percent decrease formula,
Percent Decrease = \( \left ( \frac{\text{Decreased Value}}{\text{Original Value}} \right )~\times~100\)
By substituting the values,
Percent Decrease = \( \left ( \frac{45~-~30}{\text{45}} \right )~\times~100\) [Decreased Value = Original Value – New Value]
= \( \left ( \frac{15}{\text{45}} \right )~\times~100\)
= \( \left ( \frac{1}{3} \right )~\times~100\) [Simplify]
= 33.33%
Hence, the percent decrease of the price of the hairbrush is 33.33%.
Example 2: Margaret bought 5 dozen eggs with each dozen costing $12. The next week when Margaret went to the market to buy eggs, she bought 5 dozen at $8 a dozen. What is the percent decrease in the price Margaret paid for the eggs?
Answer: As stated in the question, each dozen eggs costs $12. Hence, 5 dozen eggs cost = 5 x 12 = $60
The new price of the eggs = $8 each dozen
Total price of 5 dozen eggs = 5 x 8 = $40
According to the formula,
Percent Decrease = \( \left ( \frac{\text{Decreased Value}}{\text{Original Value}} \right )~\times~100\)
By substituting the values in the formula,
Percent Decrease = \( \left ( \frac{60~-~40}{60} \right )~\times~100\) [Decreased Value = Original Value – New Value]
= \( \left ( \frac{20}{60} \right )~\times~100\)
= \( \left ( \frac{1}{3} \right )~\times~100\) [Simplify]
= 33.33%
Hence, the percentage decrease in price of the eggs is 33.33%.
Example 3: A vegetable seller was selling potatoes at $80 a pound. In order to clear out his stock, the seller reduced the price to 5% lower than the previous cost per pound. What is the new price of the potatoes?
Answer: Let us assume that the new price of the potatoes is x.
According to the percent decrease formula,
Percent Decrease = \( \left ( \frac{\text{Decreased Value}}{\text{Original Value}} \right )~\times~100\)
It is given that percent decrease = 5%
We also know that the old value = $80 and the new value = x
Now, by rearranging the values in the formula equation,
New Value = Old Value – \( \left ( \frac{\text{Percent Decrease\( \times\)Old Value}}{100} \right )\)
x = 80 – \( \left ( \frac{5~\times~80}{100} \right )\) [Substitute the values]
x = 80 – \( \left ( \frac{400}{100} \right )\) [Apply PEMDAS rule]
x = 80 – 4 = 76
Hence, the new value of the potatoes is $76.
Yes, we can find real life examples of percent decrease around us. For example, the lowering of the price of gasoline and the lowering of the price of clothes during a Black Friday sale.
With the help of the percentage change formula, we can understand the amount of change for large databases and quantities.
The percent decrease formula is given by the percent change in the value when it is reduced over a period of time. It is expressed as a percentage.
The percent decrease formula can be written as,
Percent Decrease = [(Old Value – New Value) / Old Value] × 100]