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## Percent Decrease Formula

Percent decrease refers to the percentage change in the value when it is decreased over a period of time. For example, a decrease in the level of rainfall, a decrease in the number of Covid patients, etc. Percent decrease can be calculated by using the percent decrease formula. In this section, we will be discussing the percent decrease formula. Let us learn the percent decrease formula with a few solved examples.

## What is Percent Decrease Formula?

The percent decrease formula gives the decrease in quantity with respect to its initial value. To calculate the decrease in percentage, we first need to find the difference in the values. Then, divide the difference by the initial value and multiply it by 100. The percent decrease formula is given as:

## Percent Decrease Formula

There are two simple steps to calculate the percent decrease using the percent decrease formula, they are:

- Step 1: Find out the difference between the numbers, i.e., Decrease = Old value – New value
- Step 2: Divide the decrease by the old value and multiply it by 100. This makes the percent decrease formula,
**Percent Decrease = [(Old Value – New Value) / Old Value] × 100]**

## Percentage Increase and Decrease

Percentage increase and decrease is the percentage change in the value. Percentage change is the difference between the new value and the old value that is given. In order to find the percentage change, this difference is divided by the old value and multiplied by 100 to get the percentage increase or decrease.

Now, it should be noted that when the new value is more than the old value, then it is a percentage increase. For example, if the price of a book changes from $5 to $8, there is an increase in the price. Whereas, when the old value is greater than the new value, in that case, it is a percentage decrease. For example, if the price of a table changes from $10 to $8, there is a decrease in the price.

## Examples Using Percent Decrease Formula

**Example 1: The number 53 is misread as 35. Find the percent decrease using the percent decrease formula.**

**Solution:**

Here, new value = $35 and old value = $53

Using the Percent decrease formula, we get

Percent Decrease = [(Old Value – New Value) / Old Value] × 100

= [(53 – 35)/53] × 100

= 18/53 × 100

= 33.9%

Therefore, the percent decrease of the number is approximately 34%

**Example 2: An article whose CP is $250 was sold for $230. Use the percent decrease formula to find the percent decrease in the price of the article.**

**Solution:**

Here, new value = $230 and old value = $250

Using the Percent decrease formula, we get

Percent Decrease = [(Old Value – New Value) / Old Value] × 100

= [(250 – 230)/250] × 100

= 20/250 × 100

= 8%

Therefore, the percentage decrease in the price of the article is 8%.

**Example 3: A fruit seller used to sell strawberries for $80 per dozen. Now, he reduced the cost of a dozen strawberries by 5%. What is the price of a dozen strawberries now? Calculate by using the percent decrease formula.**

**Solution:**

Let the new value for a dozen strawberries be x.

According to the percent decrease formula,

Percent Decrease = [(Old Value – New Value) / Old Value] × 100

It is given that percent decrease = 5%; New value = x, old value = 80

So, putting these values in the equation,

5 = [(80 – x)/80] × 100

x = 76

So, the new price of a dozen of strawberries is $76.

## FAQs on Percent Decrease Formula

### What is meant by Percent Decrease?

Percent decrease refers to the percent change in the value when it is decreased over a period of time. Percentage decrease expresses the decrease in the given value with respect to its initial value in the form of a percentage.

### What is the Formula for Percent Decrease?

The percent decrease formula is formed when we find the difference between the old value and the new value, divide it by the old value and multiply it by 100. The percent decrease formula is expressed as:

Percent Decrease = [(Old Value – New Value) / Old Value] × 100]

### What are the Steps to Calculate the Percent Decrease using the Percent Decrease Formula?

There are three simple steps to calculate the percent decrease using the percent decrease formula, they are:

- Step 1: Find out the difference between the numbers, i.e., Decrease = Old value – New value
- Step 2: Divide this ‘decrease’ by the old value and multiply it by 100. This makes the percent decrease formula,
**Percent Decrease = [(Old Value – New Value) / Old Value] × 100]** - Step 3: The given values are substituted in the formula to find the percentage decrease.

### Using the Percent Decrease Formula, Calculate the Percent Decrease in the price of Pencils from $12 to $9.

We will use the percent decrease formula to calculate the percentage decrease in the price of pencils. In the given example, new value = $9 and old value = $12. Percent Decrease = [(Old Value – New Value) / Old Value] × 100. Substituting the values in the formula, Percent Decrease = [(12 – 9)/12] × 100 = 25%. Therefore, the percent decrease in the price of pencils is 25%.

### What is the Percent Decrease from 20 to 16?

The percentage decrease from 20 to 16 can be calculated using the formula, Percent Decrease = [(Old Value – New Value) / Old Value] × 100. In this case, old value = 20, new value = 16. So, after substituting the values in the formula, Percent Decrease = [(20 – 16) / 20] × 100 = 20%

### What is an Example of Percent Decrease?

Examples of percentage decrease can be seen in our day-to-day lives. Suppose the price of fuel decreases from $7 to $4. The percentage decrease of the fuel price can be calculated by using the formula, Percent Decrease = [(Old Value – New Value) / Old Value] × 100. Here, old value = 7, new value = 4. So, after substituting the values in the formula, Percent Decrease = [(7 – 4) / 7] × 100 = 42.8%

### What is the Percentage Decrease from 12500 to 11625?

The percentage decrease from 12500 to 11625 can be calculated using the formula, Percent Decrease = [(Old Value – New Value) / Old Value] × 100. In this case, old value = 12500, new value = 11625. So, after substituting the values in the formula, Percent Decrease = [(12500 – 11625) / 12500] × 100 = 7 %

## What Is Percentage Change?

Percentage change is used for many purposes in finance, often to represent the price change of a stock over time, expressed as a percentage. The formula used to calculate percentage change is a simple mathematical concept.

- Percentage change is used for many purposes in finance, most notably to track the price change of stocks and market indexes.
- It’s also used to compare the values of different currencies.
- Percentage change can also be found in balance sheets with comparative financial statements.

## Understanding Percentage Change

Percentage change can be applied to any quantity that you measure over time. In finance, the percentage change formula is often used to track the prices of both individual securities and large market indexes and compare the values of different currencies.1

Balance sheets with comparative financial statements will generally include the prices of specific assets at different points in time along with the percentage changes over the accompanying time periods. For example, a company might use percentage change to illustrate revenue growth year-over-year (YOY) in its balance sheet.

## Formula and Calculation of Percentage Change

To calculate a percentage increase, first work out the difference (increase) between the two numbers you are comparing:1

*Increase = New Number – Original Numb*er

Next, divide the increase by the original number and multiply the answer by 100:

*% Increase = Increase / Original Number × 100.*

This gives you the total percentage change, or increase.

To calculate a percentage decrease first, work out the difference (decrease) between the two numbers you are comparing.

*Decrease = Original Number – New Number*

Next, divide the decrease by the original number and multiply the answer by 100.

*% Decrease = Decrease / Original Number × 100*

The result gives you the total percentage change, or decrease.

If you want to calculate the percentage increase or decrease of several numbers, it’s best to use the formula for calculating the percentage increase. Positive values indicate a percentage increase while negative values indicate a percentage decrease.

## Example of Calculating Percentage Change

As an example of calculating percentage change consider Bob, who bought shares of a stock at $35 per share on Jan. 1. On Feb. 1, the stock was worth $45.50 per share. By what percentage did the stock increase?

To solve this calculation, first calculate the difference in price between the new and old numbers. $45.50 – $35 = $10.50 more. To work out the increase as a percentage, divide the increase by the original (January) number:

*10.5 / 35 = 0.3*

Finally, to get the percentage, we multiply the answer by 100. This simply means moving the decimal place two columns to the right.

*0.3 × 100 = 30*

The stock increased 30%.

## Percent Decrease Formula

Percentage decrease formula is the measure to identify how much a variable has lost its value. The variable can either be population, cost, profit, etc. Here, the formula for percentage decrease is given along with solved examples for better understanding of the concept.

### Formula for Percent Decrease

Percentage decrease formula can be obtained by simply dividing the decreased value by the original value and multiplying that with 100.

∴ Percent Decrease = (Decreased Value / Original Value) × 100 |

**Here,**

- Decreased Value = Original Value – New Value

### Example Questions Using Percent Decrease Formula

**Example 1:**

A shopkeeper used to sell a pair of pens for Rs. 25. He then reduced the price of the same pair of pens to Rs. 21. Calculate the percentage decrease in cost.

**Solution:**

In this question, the decrease amount is = Rs. (25 – 21) = Rs. 4

Now, the decrease in percentage = (4/ 25) × 100 = 16%

**Example 2:**

A fruit seller used to sell bananas for Rs. 40 per dozen. Now he reduced the cost of a dozen bananas by 10%. What is the price of a dozen bananas now?

**Solution:**

Let the new value for a dozen bananas be Rs. x.

Now, decrease value = Rs. (40 – x)

According to the percent decrease formula,

**% D = (Decrease/ Old value) × 100**

It is given that %D = 10.

So, putting these values in the equation,

10/100 = (40 – x)/40

=> 40 – x = 4

=> x = 36

So, the new price of a dozen of bananas is Rs. 36.

**Example 3:**

The cost of a membership card of a club was reduced by 20% and costs Rs. 550 now. What was the original price of the membership card before its cost reduced?

**Solution:**

Let the original cost be Rs. x

As the new cost is Rs. 550, decrease = Rs. (x – 550)

%D = decrease/original × 100

∴ (x – 550)/x = 20/100

So, 5x – 2750 = x

=> x = 687.5

Hence, the original price was Rs. 687.5.

### Examples – Percentage Increase and Decrease

**In January Dylan worked a total of 35 hours, in February he worked 45.5 hours – by what percentage did Dylan’s working hours increase in February?**

To tackle this problem first we calculate the difference in hours between the new and old numbers. 45.5 – 35 hours = 10.5 hours. We can see that Dylan worked 10.5 hours more in February than he did in January – this is his **increase**. To work out the increase as a percentage it is now necessary to divide the increase by the original (January) number:

**10.5 ÷ 35 = 0.3 **(See our **division** page for instruction and examples of division.)

Finally, to get the percentage we multiply the answer by 100. This simply means moving the decimal place two columns to the right.

**0.3 × 100 = 30**

**Dylan therefore worked 30% more hours in February than he did in January.**

In March Dylan worked 35 hours again – the same as he did in January (or 100% of his January hours). What is the percentage difference between Dylan’s February hours (45.5) and his March hours (35)?

First calculate the decrease in hours, that is: **45.5 – 35 = 10.5**

Then divide the decrease by the original number (February hours) so:

**10.5 ÷ 45.5 = 0.23** (to two decimal places).

Finally multiply 0.23 by 100 to give 23%. **Dylan’s hours were 23% lower in March than in February.**

You may have thought that because there was a 30% increase between Dylan’s January hours (35) and February (45.5) hours, that there would also be a 30% decrease between his February and March hours. As you can see, this assumption is incorrect.

The reason is because our original number is different in each case (35 in the first example and 45.5 in the second). This highlights how important it is to make sure you are calculating the percentage from the correct starting point.

Sometimes it is easier to show percentage decrease as a negative number – to do this follow the formula above to calculate percentage increase – your answer will be a negative number if there was a decrease. In Dylan’s case the *increase* in hours between February and March is -10.5 (negative because it is a decrease). Therefore -10.5 ÷ 45.5 = -0.23. -0.23 × 100 = -23%.

Dylan’s hours could be displayed in a data table as:

Month | Hours Worked | Percentage Change |

January | 35 | |

February | 45.5 | 30% |

March | 35 | -23% |

## Calculating Values Based on Percentage Change

Sometimes it is useful to be able to calculate actual values based on the percentage increase or decrease. It is common to see examples of when this could be useful in the media.

You may see headlines like:

UK rainfall was 23% above average this summer.

Unemployment figures show a 2% decline.Bankers’ bonuses slashed by 45%.

These headlines give an idea of a trend – where something is increasing or decreasing, but often no actual data.

Without data, percentage change figures can be misleading.

Ceredigion, a county in West Wales, has a very low violent crime rate.

Police reports for Ceredigion in 2011 showed a 100% increase in violent crime. This is a startling number, especially for those living in or thinking about moving to Ceredigion.

However, when the underlying data is examined it shows that in 2010 one violent crime was reported in Ceredigion. So an increase of 100% in 2011 meant that two violent crimes were reported.

When faced with the actual figures, perception of the amount of violent crime in Ceredigion changes significantly.

In order to work out how much something has increased or decreased in real terms we need some actual data.

Take the example of “*UK rainfall this summer was 23% above average*” – we can tell immediately that the UK experienced almost a quarter (25%) more rainfall than average over the summer. However, without knowing either what the average rainfall is or how much rain fell over the period in question we cannot work out how much rain actually fell.

Calculating the actual rainfall for the period if the average rainfall is known.

If we know the average rainfall is 250mm, we can work out the rainfall for the period by calculating 250 + 23%.

First work out 1% of 250, 250 ÷ 100 = 2.5. Then multiply the answer by 23, because there was a 23% increase in rainfall.

2.5 × 23 = 57.5.

**Total rainfall for the period in question was therefore 250 + 57.5 = 307.5mm.**

Calculating the average rainfall if the actual amount is known.

If the news report states the new measurement and a percentage increase, “*UK rainfall was 23% above average… 320mm of rain fell…*”.

In this example we know the total rainfall was 320mm. We also know that this is 23% above the average. In other words, 320mm equates to 123% (or 1.23 times) of the average rainfall. To calculate the average we divide the total (320) by 1.23.

320 ÷ 1.23 = 260.1626. *Rounded to one decimal place, the average rainfall is 260.2mm.*

The difference between the average and the actual rainfall can now be calculated:

320 – 260.2 = **59.8mm**.

We can conclude that 59.8mm is 23% of the average rainfall amount (260.2mm), and that in real terms, 59.8mm more rain fell than average.

## What is percentage decrease?

Percentage decrease is the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.

For instance, if you spent $200 to heat your home last month, but only $140 this month, the cost has decreased by $60. Expressed as a percentage decrease, you can conclude the cost of heating your home has decreased by 30%.

## How to calculate percentage decrease

Use these steps and formula to calculate percentage decrease:

Percentage decrease = (starting value – ending value)/starting value x 100

- Determine the starting value and ending value.

For example, Joe is considering changing jobs. He works for a company making $22.75 per hour. He has been offered a position closer to home that pays $20.50 per hour. To find the percentage decrease in pay: - Subtract the ending value from the starting value.

*Using the example above, subtract the new rate of pay from the original rate of pay. $22.50 – $20.20 = $2.25* - Divide this number by the starting value.

*Divide this number, the difference between rates of pay, by the original rate of pay. $2.25 / $22.50 = .1* - Multiply by 100 to find the percentage change (Note: if the percentage is a negative, this means the percentage change is positive.)

*Multiply this number by 100 to determine the percentage decrease. .1 x 100 = 10% decrease*

If Jose takes the new job, his pay would decrease by 10%.

## Examples of how to calculate percentage decrease

The following examples show how to solve for percentage decrease when given a starting and ending value:

**Example 1**

Brenda scored an 87 on her first biology test and an 82 on her second biology test. To find the percentage decrease between test scores:

- *Subtract the new test score from the old test score. 87 – 82 = 5*
- *Divide the difference of the two scores by the original test score. 5 / 87 = .057 (rounded)*
- *Multiply this number by 100 to determine the percentage decrease. .057 x 100 = 5.7%*

The rate of percentage decrease between Brenda’s test scores was 5.7%.

**Example 2**

Dianne averaged 70 mph driving to St. Petersburg. On the return trip during rush hour, she averaged 54 mph. To find the percentage decrease in her rate of travel:

- *Subtract the new rate of travel from the original rate of travel. 70 mph – 54 mph = 16 mph*
- *Divide this difference by the original rate of travel. 16mph / 70mph = .229 (rounded)*
- *Multiply this quotient by 100 to determine the decrease as a percentage. .229 x 100 = 22.9%*

The decrease in the rate of travel between trips was 22.9%. Dianne traveled 22.9% more slowly on her second trip.

**Example 3**

If the results indicate a negative percentage decrease, this means the rate of change is positive. This is most likely to occur as a result of misunderstanding the problem. When calculating for a rate of decrease between an original cost of $75 and a new cost of $80:

- *Subtract the second cost from the original cost. $75 – $80 = -$5*
- *Divide the difference by the original cost. -5 / 75 = -.067*
- *Multiply by 100 to express the number as a percent. -.067 x 100 = -6.7%*
- Recognize the negative means that the answer is the opposite of a rate of decrease. Instead, it expresses a rate of increase.

In this case, the rate of cost increase is 6.7%.

## How to calculate value based on percentage decrease

Use the following steps and formula to calculate value based on percentage decrease:

New value = original value – (percentage decrease/100 x original value)

You may know the percentage decrease and the starting value but want to find the ending value. For example, you might consider paying a service fee of $9.75 per month for a streaming service running a promotion of a 20% discount for one month. The discounted rate would be $7.80 for the first month. Here’s how to calculate this:

- Convert the percentage decrease into a decimal by dividing by 100.
- Multiply the resulting decimal by the starting value.
- Subtract this value from the starting value.
- This is the new value based on the given percentage decrease.

Much like in the previous examples, the most common errors involve arithmetic. In the case of calculating value based on percentage decrease, the most common is forgetting to subtract the change in value from the original.

## Examples of how to calculate value based on percentage decrease

The following examples include the steps to finding a new value when given a starting value and the percentage decrease:

**Example 1**

Crystal uses a home cleaning service that charges $125 per visit. She receives a coupon for 30% off her next home cleaning. To find the cost of her next home cleaning:

- *Convert the percentage decrease into a decimal by dividing by 100. 30% / 100 = .30*
- *Multiply the original cost by the decrease to find the value of the discount. .30 x $125 = $37.50*
- *Subtract the value of the discount from the original cost. $125.00 – $37.50 = $87.50*

By using the percentage decrease, the cost of Crystal’s next home cleaning is $87.50 and, further, her savings is $37.50.

**Example 2**

Deondre pays $114 per month for his cell phone. He sees an advertisement that a cellular provider will beat his existing monthly rate by 25%. To find the new provider’s rate:

- *Convert the percentage decrease into decimal form by dividing by 100. 25% / 100 = .25*
- *Multiply this decimal by the original cost to determine the discounted rate. $114 x .25 = $28.50*
- *Subtract the discount from the original cost to determine the new rate. $114.00 – $28.50 = $85.50*

Deondre’s new rate will be $85.50 per month. His savings is $28.50 per month.

**Example 3**

One year ago, Andrea bought a new car for $21,350. Her accountant tells her it has lost 17% of its value since then. To find the value of Andrea’s car now:

- *Convert the percentage decrease into decimal form by dividing by 100. 17% / 100 = .17*
- *To determine the loss of value multiply this decimal by the original cost. $21,350 x .17 = $3,629.50*
- *Subtract the loss of value from the original value. $21,350 – $3,629.50 = $17,720.50*

Andrea’s car is now worth $17,720.50. Her car lost $3,629.50 in value, or depreciated, over the first year.

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