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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 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.

Question for Important Formula: Percentages
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What is the formula to calculate percentage?
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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

The document Important Formula: Percentages | CSAT Preparation - UPSC is a part of the UPSC Course CSAT Preparation.
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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 can use the formula: (Part/Whole) x 100. Simply divide the part by the whole number, then multiply the result by 100 to get the percentage.
2. How can you calculate percentage increase and decrease?
Ans. To calculate percentage increase, subtract the original number from the new number, then divide the result by the original number and multiply by 100. To calculate percentage decrease, follow the same steps but subtract the new number from the original number.
3. What is the importance of understanding percentages?
Ans. Understanding percentages is important in everyday life as it helps in calculating discounts, taxes, tips, and interest rates. It also allows for easy comparison of values and identifying trends in data.
4. Can percentages be used to compare different quantities?
Ans. Yes, percentages can be used to compare different quantities by converting them into a common percentage scale. This allows for a more straightforward comparison of values regardless of their initial amounts.
5. How can percentages be helpful in budgeting and financial planning?
Ans. Percentages are crucial in budgeting and financial planning as they help in allocating funds, setting savings goals, and tracking expenses. By using percentages, individuals can create a realistic financial plan and monitor their progress effectively.
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