 # Percentage Increase Decrease

## What is Percentage Increase or Percentage Decrease?

 (image will be uploaded soon) Change: For calculating the changes subtract the old value from the new value.For example: Suppose if you had 5 books, but now have 7 books. The change in the number of books is: 7 − 5 = 2. (image will be uploaded soon) Percentage Change: Percentage change basically show that change as a percent of the old value so we need to divide by the old value and convert it into a percentage:So the percentage change from 5 to 7 can be written as: 2/5 = 0.4 And when 0.4 is multiplied by 100 we get a percentage= 40%

Decrease basically means to lower or go down. Suppose if you are driving above the speed limit, you should decrease your speed .Students always want their teachers to decrease the amount of homework they give their students. Decrease is the opposite of increase. In simple words, increase means to increase and decrease means to lower.

### Steps to Calculate Percentage Increase:

To calculate the percentage increase you need to follow these steps-

Step 1) First you need to work out the difference (increase) between the two numbers that you are comparing.

Formula to find the increase is,

Increase = New Number - Original Number

Step 2) Now, you need to divide the increase by the original number and multiply the answer you get by 100.

Percentage increase = $\frac{\text{Increase}}{\text{Original Number}}$ × 100.

Step 3) If your answer is a negative number, then this is a percentage decrease.

### Steps to Calculate Percentage Decrease:

To calculate the percentage decrease you need to follow these steps-

Step 1) First, you need to work out the difference (that is the decrease) between the two numbers that you are comparing.

Formula to find the increase is,

Decrease = Original Number - New Number

Step 2) Then, you need to divide the decrease by the original number and multiply the answer you get by 100.

$\text{Percentage decrease} = \frac{\text{Decrease}}{\text{Original Number}}$ × 100

Step 3) If the answer you get is a negative number, then this is a percentage increase.

NOTE: Now, if you wish to calculate the percentage increase or percentage decrease of several numbers then we recommend using the first formula. The positive values basically indicate a percentage increase whereas negative values indicate a decrease in the percentage.

### Examples for Better Understanding!

Example 1) The price of a pair of socks went from $\$5 to $\$6, what will be the percentage change?

Answer) There are two methods to solve this question, let’s go through both of them,

(Method 1):

• Step 1: $\$5 to $\$6 there is a $\$1 increase

• Step 2: Now, let’s divide by the old value: $\frac{\1}{\5}$  which is equal to 0.2

• Step 3: You can convert 0.2 to percentage by multiplying it by 100: 0.2 × 100 = 20% rise.

(Method 2):

• Step 1: First you need to divide new value by old value: $\frac{\6}{\5}$ which is equal to 1.2

• Step 2: Now, convert to percentage: 1.2 × 100 = 120% (that is $\$6 is 120% of $\$5)

• Step 3: Lastly, subtract: 120% − 100% = 20%, and that means a 20% rise.

### Formula to Find the Increase/Decrease in Percentage:

You can also put the values into this given formula:

(New Value of any item − Old Value of the item)/ |Old Value of the item| × 100%

(The "|" symbols mean it gives us the absolute value, so that the negatives become positive)

For example: There were 200 customers yesterday, and there are 240 customers today:

$\frac{(240 - 200)}{|200|}$ × 100% = $\frac{40}{200}$ × 100% = 20%

Therefore, we get a 20% increase.

Some people think that a percentage increase can be "reversed" by the same percentage decrease, but this is not true.

Now to "reverse" a percentage rise or fall, you can use the right formula here:

## How to Reverse a Rise or Fall ?

 How to Reverse: Use this Percent: Example 10% An "x" percent rise equal to: $\frac{x} {(1 + \frac{x}{100})}$ $\frac{10} {(1 + \frac{10}{100})}$ = $\frac{10}{(1.1)}$ = 9.0909. An "x" percent fall equal to : $\frac{x} {(1 - \frac{x}{100})}$ $\frac{10} {(1 - \frac{10}{100})}$ = $\frac{10}{(0.9)}$ = 11.111.

### Questions to be Solved:

Question 1) The annual salary of Suresh increased from Rs 1, 80,000 to Rs 2, 20,000. Find the percentage increase in the price.

Solution) Original salary = Rs 1, 80,000

Increased salary = Rs 2, 20,000

Increase in salary = Rs 2, 20,000- Rs 1, 80,000 = Rs 40,000

Thus, $\text{percentage increase in salary} = \frac{\text{increase in salary}}{\text{original salary}}\times 100 = \frac{40,000}{1,80,000}\times 100$ that is equal to 22.2.

Question2) How do you find the percent of decrease?

Answer) Here are the steps to find the percent of decrease -

Step 1) First, subtract starting value minus final value.

Step 2) Next step, you need to divide that amount by the absolute value of the starting value.

Step 3) In step 3, multiply it by 100 to get percent decrease.

Step 4) Now, if the percentage we have is negative, then it means there was an increase and not a decrease.

Question 1)What is the Formula of Percentage and What is Increase and Decrease?

Answer) Suppose, if you have to turn a percentage into a decimal, then you need to just divide by 100. Here’s for an example, 25% = 25/100 that is equal to 0.25. If you want to change a decimal into a percentage, then you need to multiply by 100. So let’s take for example we have to convert 0.3 into percentage then 0.3 = 0.3 × 100 = 30%.

Decrease basically means to lower or go down. Suppose if you are driving above the speed limit, you should decrease your speed .Students always want their teachers to decrease the amount of homework they give their students. Decrease is the opposite of increase. In simple words, increase means to increase and decrease means to lower.

Question 2)What is Percent of Change and What is the Formula to Find the Increase?

Answer)Percent of change can be defined as a comparison between two values expressed in hundredths. A negative percent of change basically indicates a decrease from the original value to the new value. A positive percent change basically indicates an increase from the original value to the new value.You can also put the values into this given formula:

(New Value of any item − Old Value of the item)/ |Old Value of the item| × 100%

(The "|" symbols mean it gives us the absolute value, so that the negatives become positive)

For example: There were 200 customers yesterday, and there are 240 customers today:

(240 – 200)/ |200| × 100% = 40/200 × 100% = 20%

Therefore, we get a 20% increase.