Percent Decrease Formulas | List of Percent Decrease Formulas You Should Know - BYJUS

# Percent Decrease Formulas

Percentage decrease can be defined as the change in a specific value as it is decreased over a period of time. The formula for percent decrease is highly useful for finding out how much a particular item has lost its value....Read MoreRead Less

### 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.