General Aptitude: Percentages

Formulas of Percentage

Percentage: The percentage is a way of expressing a fraction or a ratio in terms of parts per hundred. It is denoted by the symbol "%." The formula to calculate the percentage is:

Percentage = (Part/Whole) x 100

Increase/Decrease by Percentage:

Increase by Percentage: New Value = Original Value + (Original Value x Percentage/100)

Decrease by Percentage: New Value = Original Value - (Original Value x Percentage/100)

Shortcuts of Percentage

Converting Fractions to Percentages: To convert a fraction to a percentage, multiply the fraction by 100. The numerator of the fraction represents the part, and the denominator represents the whole.

Calculation of 10%: To calculate 10% of a value, divide the value by 10. For example, 10% of 200 is 20 (200/10 = 20).

Calculation of 1%: To calculate 1% of a value, divide the value by 100. For example, 1% of 500 is 5 (500/100 = 5).

Points to Remember About Percentage

Major points that we need to cover while studying Percentage:

Percent implies “for every hundred”.
The percentage is denoted by “%”. Ex: x% is read as ‘x percent’.
Conversion of fraction or a decimal into a percent.
Converting a percentage into a fraction.
Converting fractions into percentages.
Fraction of a fraction and relative percentage.
Successive percentage change.
Formulae for a percentage increase or decrease.
x% of y = x ÷ 100 x y

Examples of Percentage

Ex: ? = 20% of 80

Sol: ? = 20/100 x 80 = 16

x% of y = y% of x

This concept is very helpful, let see an example.

Ex: ? = 48% of 50

Sol: ? = 48% of 50 = 50% of 48 = 48 / 2 = 24

What percentage of x is y = y / x × 100

Ex: 30 is what percent of 48?

Sol: 30 / 48 × 100= 62.5%

Percentage change = Change / Initial value × 100

Ex: If the price of soap has changed from Rs. 24 to Rs. 30, what is the percent change in the price of the soap?

Sol: Answer = (30 - 24) / 24 × 100 = 25%

Percentage point change = Difference of two percentage

Ex: If the pass percentage in an exam was 60 % in 2017 and 75% in 2018, then Percentage point change = Final percentage – Initial percentage = 75% – 60% = 15%

Ex: Passing percentage in an exam of total marks 600 is 60%. The passing percentage has been increased by 15% point, then new passing percentage

Sol: Old passing percent = 60% and the new passing percent = 60% + 15% = 75% (Not 60% + 15% of 60% = 60% + 9% = 69%)

If a number x increases by y%, then the new number = x(1+ y / 100)

Ex: Monthly salary of Ramesh in 2018 was Rs.56000 and it increases by 20% in 2019, then his monthly salary in 2019 will be

Sol: Monthly salary of Ramesh in 2019 = 56000(1+ 20 / 100) = Rs.67200.

If a number x decreases by y%, then the new number = x(1 – y / 100)

Ex: Monthly salary of Ramesh in 2018 was Rs.56000 and it decreases by 20% in 2019, then his monthly salary in 2019 will be

Sol: Monthly salary of Ramesh in 2019 = 56000(1 – 20 / 100) = Rs. 44800

If the value of an item/number goes up by x%, the percentage reduction to bring it back to the original point = x / (100 + x) × 100%.

Ex: Price of soap is Rs. 40. It is increased by 25%, then by what percent the price of the soap should be decreased to make the price of the soap Rs. 40.

Sol: Required percentage = 25 / (100 + 25) × 100 = 20%.

If the value of an item/number goes down by x%, the percentage increment to bring it back to the original point = x / (100 - x) × 100%.

Ex: Price of soap is Rs. 40. It is increased by 25%, then by what percent the price of the soap should be decreased to make the price of the soap Rs. 40.

Sol: Required percentage = 25 / (100 – 25) × 100 = 33full 1/3%.

If A is x% more than B, then B is [x / (100 + x) × 100]% less than A.

Ex: A is 30% more than B, then B is what percent less than A?

Sol: Required percentage = 30 / (100 + 30) × 100 = 23full 1/13%.

If A is x% less than B, then B is [x / (100 - x) × 100]% less than A.

Ex: A is 30% less than B, then B is what percent more than A?

Sol: Required percentage = 30 / (100 - 30) × 100 = 42full 6/7%.

Percentage – Ratio Equivalence:

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FAQs

How to calculate Percentage?

To calculate percentages, you typically use the following formula:

(Percentage / 100) × Value = Result

Why are percentages out of 100?

The reason percentages are out of 100 is because "percent" literally means "per hundred" or "out of a hundred." So when you express a quantity as a percentage, you are comparing it to a whole of 100 units. By dividing the value by 100, you can easily calculate the proportionate amount and express it as a percentage. It provides a standardized way of representing fractions or proportions in relation to a whole.

How to calculate a Percentage Increase?

To calculate a percentage increase, you can use the following formula:

(Change in Value / Original Value) × 100 = Percentage Increase

How to calculate a Percentage Decrease?

To calculate a percentage decrease, you can use the following formula:

(Change in Value / Original Value) × 100 = Percentage Decrease

What are the 3 elements of percent?

The three elements of a percent are:

The numerator or "part": This represents the quantity or value that you are referring to. It is typically the value you want to express as a percentage.
The denominator or "whole": This represents the total or the whole from which the numerator is a part of. It provides the context or reference point for the percentage calculation.
The percent sign (%): This symbol is used to denote that the value is being expressed as a percentage, which is a fraction or proportion out of 100.