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**Percentage Decrease Formula**

**Introduction:**

Percentage decrease refers to the reduction in value expressed as a percentage of the original value. It is calculated by finding the difference between the original value and the new value, dividing it by the original value, and then multiplying by 100. Percentage decrease is commonly used to analyze changes in prices, quantities, or values over time.

**What is Percentage Decrease?**

Percentage decrease is a mathematical concept used to measure the reduction in value or quantity from an initial value to a final value. It is often employed in various fields such as finance, business, economics, and data analysis. The percentage decrease formula allows us to calculate the relative decrease as a percentage of the original value.

**Percentage Decrease Formula?**

The formula for percentage decrease is:

Percentage Decrease = ((Initial Value – Final Value) / Initial Value) x 100

In this formula, the initial value represents the starting value or the original quantity, and the final value represents the reduced value or the quantity after the decrease.

To calculate the percentage decrease, we subtract the final value from the initial value to determine the decrease in value. Then, we divide the decrease by the initial value and multiply by 100 to express it as a percentage.

For example, let’s say the initial value of a product is ₹100 and it is reduced to ₹80. Using the percentage decrease formula, we can calculate the decrease as follows:

Percentage Decrease = ((₹100 – ₹80) / ₹100) * 100 = (₹20 / ₹100) * 100 = 20%

Therefore, the percentage decrease in this example is 20%, indicating that the value of the product has decreased by 20% from its original value.

Understanding the percentage decrease formula is valuable in analyzing changes, evaluating trends, comparing data sets, and making informed decisions based on the relative decrease in values. It provides a quantitative measure to assess the extent of reduction and is a fundamental tool in various quantitative disciplines.

**Solved Examples on Percentage Decrease Formula:**

**Example 1: **A shirt originally priced at ₹800 is now on sale for ₹600. Calculate the percentage decrease in price.

Solution:

Percentage Decrease = ((Initial Value – Final Value) / Initial Value) × 100

Percentage Decrease = ((₹800 – ₹600) / ₹800) × 100 = (₹200 / ₹800) × 100 = 25%

The price of the shirt has decreased by 25%.

**Example 2: **The population of a town was 10,000 last year. This year, the population decreased to 8,000. Find the percentage decrease in population.

Solution:

Percentage Decrease = ((Initial Value – Final Value) / Initial Value) × 100

Percentage Decrease = ((10,000 – 8,000) / 10,000) × 100 = (2,000 / 10,000) × 100 = 20%

The population has decreased by 20%.

**Example 3:** A company had a profit of ₹50,000 last year. This year, the profit decreased to ₹30,000. Calculate the percentage decrease in profit.

Solution:

Percentage Decrease = ((Initial Value – Final Value) / Initial Value) × 100

Percentage Decrease = ((₹50,000 – ₹30,000) / ₹50,000) × 100 = (₹20,000 / ₹50,000) × 100 = 40%

The profit has decreased by 40%.

**Frequently Asked Questions on Percentage Decrease Formula:**

1: How to calculate percentage decrease?

Answer: To calculate the percentage decrease, subtract the new value from the old value to find the decrease. Then divide the decrease by the old value and multiply by 100 to express it as a percentage. The formula is: Percentage Decrease =((Old Value – New Value) / Old Value) x 100.

2: What is a 10 percent decrease?

Answer: A 10 percent decrease refers to reducing a value by 10 percent of its original amount. In other words, it signifies reducing a quantity by one-tenth (1/10) of its initial value. For example, if an item originally cost ₹100 and experiences a 10 percent decrease, its new price would be ₹90, reflecting the reduction of 10 percent from the original amount.

3: How do you calculate percentage change?

Answer: To calculate the percentage change, subtract the old value from the new value to find the difference. Then divide the difference by the old value and multiply by 100 to express it as a percentage. The formula is: Percentage Change =((New Value – Old Value) / Old Value) x 100.

4: What is the Difference Between Percentage Increase and Percentage Decrease?

Answer: Percentage increase is the increase in the initial value of a quantity over a period of time in percentage form. On the other hand, the percentage decrease gives the decrease in the initial value over a period in percentage form.

5: How to do 20% decrease?

Answer: To perform a 20 percent decrease, follow these steps:

Calculate the amount you want to decrease by multiplying it by 20 percent (0.20).

Subtract the result from the original amount.

For example, let’s say you have a product that originally costs ₹100. To decrease the price by 20 percent:

Multiply ₹100 by 0.20: ₹100 × 0.20 = ₹20.

Subtract ₹20 from ₹100: ₹100 – ₹20 = ₹80.

So, a 20 percent decrease in the price of the product would bring it down to ₹80.

6: What is the formula for increase percent and decrease percent?

Answer:

The formula for calculating the increase percent is:

Increase Percent = (Increase Amount / Original Value) x100

The formula for calculating the decrease percent is:

Decrease Percent = (Decrease Amount / Original Value) x 100

In both formulas, the “Increase Amount” is the difference between the new value and the original value, and the “Decrease Amount” is the difference between the original value and the new value. The “Original Value” refers to the initial value before the increase or decrease. By applying these formulas, you can determine the percentage increase or decrease in a given value.

7: What is an example of a percentage decrease?

Answer: An example of a percentage decrease is as follows:

Let’s say the original price of a product is ₹100. After a sale, the price is reduced by 20%. To calculate the new price, we can apply the percentage decrease formula.

Percentage Decrease = (Decrease Amount / Original Value) × 100

In this case, the decrease amount is 20% of ₹100, which is ₹20.

Percentage Decrease = (20 / 100) × 100 = 20%

So, the percentage decrease in the price is 20%. The new price of the product would be ₹100 – ₹20 = ₹80.

Therefore, the product has experienced a 20% decrease in price, resulting in a new price of ₹80.

8: What is the difference between percent and percent decrease?

Answer: Percent refers to a proportion or ratio out of 100, representing a portion or fraction of a whole. It is a general term used to express values, quantities, or rates relative to a base of 100.

Percent decrease, on the other hand, specifically measures the reduction or decrease in a value, quantity, or rate compared to its original value. It calculates the change in percentage between the original value and the decreased value, providing a quantifiable measure of the decrease.