Percentage Increase and Decrease Explained

The percentage refers to something out of 100. The percentage increases and decreases refer to a simple change of a variable denoted as a percentage (%). The percentage refers to a figure stated as a fraction of a hundred. So when you say "100% of anything," you're referring to the entire item. When comparing amounts, the percentage is employed. Let's assume you need to determine if the value of a given quantity has increased or decreased over time; rather than quoting figures, this comparison might be stated as a % rise or reduction in quantity. There are two types of Percentage, Percentage Increase and Percentage Decrease. The steps to the calculations are explained below.

What is a Percentage Increase?

The process of calculating the difference between something's original value and an increased one is referred to as a percentage increase. The relative increase versus the original value is then calculated using this difference and expressed as a percentage. One can use the formula to calculate the percentage increase noted below:

Calculate Percentage increase = \[\frac{\text{Increase value}}{\text{Original value}}\times 100\]

Percentage Increase:

The process of calculating the difference between something's original value and an increased one is referred to as a percentage increase. The relative increase versus the original value is then calculated using this difference and expressed as a percentage. One can use the formula to calculate the percentage increase noted below:

Percentage increase = \[\frac{\text{Increase }}{\text{Original number}}\times 100\]

What is Percentage Decrease?

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. The decrease is the opposite of the increase. In simple words, increase means to increase and decrease means to lower. 

Percent Decrease =\[ \left [ \frac{\text{(Old value -New value)}}{\text{Old value}} \right ]\times 100\]

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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.

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.

Percentage decrease = \[\frac{Increase}{Original Number}\times 100\]

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:  $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:  $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:

\[\frac{\text{(New Value of any item - Old Value of the item)}}{\left |\text{Old Value of the item}  \right |}\times 100%\]

(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:

\[\frac{(240-200)}{\left | 200 \right |}\times 100 % = \frac{40}{200}\times 100% = 20%\]

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:

What is Percentage Rise or Fall?

Working backwards to obtain an initial quantity given a percentage of that amount is known as reverse percentages (or inverse percentages).

Using a calculator, we can find 100 percent by taking the percentage we've been given, dividing it by 1 per cent, and multiplying it by 100.

We can compute this without using a calculator if we use factors from the percentage we were given.

We are occasionally given a percentage of an amount and must determine what the original value was

It's important to remember that the original payment represents 100% of the value.

How to use Reverse Percentage?

One must Write down the percentage and put it equal to the amount that they have been given.

Divide both sides by the percentage.

(e.g. if you have 80%, divide both by 80). This will give you 1%.

Multiply both sides by 100.

This will give you 100%.

How to Reverse a Rise or Fall?

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,

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 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.