[Maths Class Notes] on Percentage Formula Pdf for Exam

There are various formulas to find a percentage that helps in solving percentage problems. Imagine the most basic percentage formula: P% × A = B. However, there are many mathematical variations of the percentage calculation formulas. Let’s take a look at the three basic percentage problems that can be solved using percentage formulas. ‘A’ and ‘B’ are numbers and P is the percentage:

For example, 25% of 1000 is 250

[frac{is}{of}] = %/100 or [frac{part}{whole}] = %/100

Percentage Formula

How to Find what percent (%) of A is B.

Example: What percent of 75 is 15?

Follow the below step-by-step procedure and solve percentage problem in one go

1. First, you will require to convert the problem to an equation using the formula of percentage i.e. A/B = P%

2. Do the math, since A is 75, B is 15, so the equation becomes: 15/75 = P%

3. Solve the equation: 15/75 = 0.20

4. Note! The outcome tends to be always in decimal form, not a percentage. Therefore. We will require multiplying the outcome by 100 to obtain the percentage.

5. Convert the decimal 0.20 to a percent multiplying it by 100

6. We get 0.20 × 100 = 20%

So 20% of 75 is 15

How to Find A if P percent of it is B

Example: 50 are 10% of what number?

 Follow the below step-by-step procedure and solve percentage problem in one go

1. First, convert the problem to an equation using the formula of percentage i.e. B/P% = A

2. Given that value of ‘B’ is 50, P% is 10, so the equation is 50/10% = A

3. Convert the percentage to a decimal form, dividing by 100.

4. Converting 10% to a decimal brings us: 10/100 = 0.10

5. Substitute 0.10 for 10% in the equation: 50/0.10 = A

6. Do the math: 50/0.10 = A

A = 500

So 50 is 10% of 500

Percentage Difference Formula

The percentage difference between the two values/numbers is reckoned by dividing the absolute value of the difference between the two values by the average of those two values. Multiplying the outcome by 100 is purposed to produce the solution in the form of percent, rather than in decimal. Take a look at the below equation for an easy explanation;-

Percentage Difference formula = |A1 – A2|/ (A1 + A2)/2× 100

For example: find out the percentage difference between two values of 20 and 4

Solution: given two values is 20 and 4

So,

|20 – 4| / (20 + 4)/2 × 100

= 4/3 × 100

= 1.33 × 100

= 133.33%

Percentage Change Formula

Percentage decrease and increase are reckoned by determining by the difference between two values and comparing that difference to the primary value. With respect to mathematical concepts, this involves considering the absolute value of the difference between two values and dividing the outcome by the primary value, typically computing how much the primary value has changed.

The percentage change calculator computes an increase or decrease of a definite percentage of the input number. It typically takes into account converting a percent into its decimal equivalent, and either adding or subtracting the decimal equivalent from and to 1, respectively. Multiplying the primary number by this value will lead to either an increase or decrease of the number by the given percent. Refer to the example below for clarification.

Refer to the below equation for easy explanation:-

Example: 700 increased by 20% (0.2)

700 × (2 + 0.2) = 840

700 decreased by 10%

700 × (1 – 0.1) = 630

Solved Examples

Example1

Find out ___% of 15 is 6

Solution1

Here whole = 15 and part = 6, but % is missing

We obtain:

6/15 = %/100

Replacing % by x and cross-multiplying provides:

6 × 100 = 15 × x

600 = 15 × x

Divide 600 by 15 to get x

600/15 = 40, so x = 40

Thus, __40_% of 15 is 6

Example2

The tax on a soap dispenser machine is Rs 25.00. The tax rate is 20%. What is the price without tax?

Solution2

P × 20/100 = 25

= 20/100 equal 5

Solve the equation multiplying both sides by 100 and then dividing both sides by 20.

The price without tax is Rs. = 125

Fun Facts

1. The percentage (%) sign bears a significant ancient connection. Ancient Romans often performed calculations in fractions dividing by 100, which is presently equivalent to the computing percentages.

2. Calculations with a denominator of 100 became more typical since the introduction of the decimal system.

3. Percentage methods had frequently been used in medieval arithmetic texts to describe finances, such as interest rates.