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Important Formula: Percentages | CSAT Preparation - UPSC PDF Download

Percentage

Percentage basically means a part per hundred. A fraction whose denominator is 100 is called a percentage .

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100.

Percentage formula = (Value/Total value) × 100

Important Formula: Percentages | CSAT Preparation - UPSC

It is represented by % symbol. In all the fractions where the denominator is 100 we remove the denominator and put the % sign.

Calculating the Percentage of a Number

To calculate the percentage of a number, we need to use a different formula such as:

P% of Number = X

where X is the required percentage.

If we remove the % sign, then we need to express the above formulas as;

P/100 * Number = X

Important Formula: Percentages | CSAT Preparation - UPSC

Let us understand with help of some examples.

Example: Calculate 10% of 80.
Solution:Let 10% of 80 = X

10/100 * 80 = X

X = 8

Example:The number 450 is what percentage of 1200?
Solution: = (450/1200) × 100

By simplifying the fraction, we get

= (3/8) × 100 

= 0.375 × 100

= 37.5%

So, the number 450 is 37.5% of 1200.

Example: Convert 0.32 to percentage.
Solution:Multiplying 0.32 by 100, we get 0.32 × 100 = 32% as the answer.

Example: Convert the fraction 23/25 to percentage.
Solution: Converting 23/25 to a decimal value, we get 0.92. 

So, 0.92 × 100 = 92% is the answer.

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Percentage Increase and Decrease

(i) Percentage Increase

The percentage increase is equal to the subtraction of the original number from a new number, divided by the original number and multiplied by 100.

Important Formula: Percentages | CSAT Preparation - UPSC

% increase = [(New number – Original number)/Original number] x 100

where, increase in number = New number – original number

(ii) Percentage Decrease

Similarly, a percentage decrease is equal to the subtraction of a new number from the original number, divided by the original number and multiplied by 100. 

Important Formula: Percentages | CSAT Preparation - UPSC

% decrease = [(Original number – New number)/Original number] x 100

Where decrease in number = Original number – New number

(iii)Percentage Formula in terms of a Fraction

To transform a fraction into a percentage divide the top/numerator number by the bottom/denominator number and lastly multiply the result by 100%.

Important Formula: Percentages | CSAT Preparation - UPSC

(iv)Percentage Change Formula

Sometimes when it is required to get the increase or decrease in any quantity as percentages, which is also directed to as percentage change is given by the formula:


Important Formula: Percentages | CSAT Preparation - UPSC

How to Find Percentage?

To estimate the percentage of any value/ data/ number, we can apply the various formulas as discussed above as per the condition applied. Let us learn the basic method to find the percentage.

A% of a data = B
Here B is the necessary percentage.
If we wish to remove the % sign, then the formula is expressed as:
A/100 * given data = B
For example: How to calculate 20% of 60.
Let 20% of 60 = Y
20/100 * 60 = Y
Y = 12

Similarly; 8% means 8 out of every 100, or in fraction we write 8/100.
In the same way, 50% can be composed as a fraction, 1/2, or a decimal, 0.5.

Percentage Table

Some common fraction and their percentages equivalents are given below.

Important Formula: Percentages | CSAT Preparation - UPSC

How to Convert Fractions to Percentages?

A fraction can be represented by x/y  and can be converted into percentage by the below formula: x/y * 100

Therefore by the formula, it is clear that we can convert fraction to percentage merely by multiplying the given fraction by 100.

Note: To convert percentages into fraction, divide it by 100.
Example: 25% = 25/100 = ¼
To convert a fraction into percentage, multiply in by 100.

Difference between Percentage and Percent

  • The terms percentage and percent are closely related.
  •  The use of percent (or the symbol %) is always paired with a specific number.
  • On the other hand, percentage is used without a number.
  •  Example of percent: 
    • More than 65% of the country's population has received the first dose of the Covid-19 vaccine.
  • Example of percentage:
    •  A very large percentage of the world's population has been affected by the Covid-19 pandemic. 

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FAQs on Important Formula: Percentages - CSAT Preparation - UPSC

1. How do you calculate the percentage of a number?
Ans.To calculate the percentage of a number, you multiply the number by the percentage (expressed as a decimal). For example, to find 20% of 50, you would calculate 50 * 0.20 = 10.
2. What is the formula for calculating percentage increase?
Ans.The formula for calculating percentage increase is: ((New Value - Old Value) / Old Value) * 100. This gives you the increase as a percentage of the original value.
3. How do you find the percentage decrease?
Ans.To find the percentage decrease, you use the formula: ((Old Value - New Value) / Old Value) * 100. This will tell you how much the value has decreased relative to the original amount.
4. What is a simple way to express a percentage as a fraction?
Ans.To express a percentage as a fraction, you can place the percentage number over 100 and simplify if possible. For example, 25% can be expressed as 25/100, which simplifies to 1/4.
5. Can you explain how to convert a decimal to a percentage?
Ans.To convert a decimal to a percentage, you multiply the decimal by 100 and add the percent symbol. For example, 0.75 converted to a percentage would be 0.75 * 100 = 75%.
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