Percentage

In mathematics, a percentage is a figure or ratio that signifies a fraction out of 100, i.e., A fraction whose denominator is 100 is called a Percent. In all the fractions where the denominator is 100, we can remove the denominator and put the % sign.

For example, the fraction 23/100 can be written as 23%. The opposite of this is also true, i.e., any percentage sign can be easily replaced by converting the number into a fraction with the denominator 100. For example, 45% can be converted to a fraction as 45/100.

Percentage Formula

The percentage formula is a formula that is used to find the amount or share of a quantity in terms of a hundred. So, for calculating the percentage, we need three variables. First, the total value V₁, the present value V₂, and the percentage value P. The algebraic equation for this will be:

Percentage (P%) = (Parts (V₂) / Whole (V₁)) × 100

How to Calculate the Percentage of a Number?

Calculating the percentage of a number is very simple, you just need to use the formula mentioned below:

Percent of a Number = Percentage/100 × Number

Example: Calculate 5% of 50

• 5% of 50 = 5/100 × 50
• 5% of 50 = 0.05 × 50
• 5% of 50 = 2.50

Percentage Calculator

The Percentage Calculator is a free tool prepared at GeeksforGeeks that is used to find the percentage if two or more numbers are given. Check the percentage calculator below:

Percentage Difference Formula

The Percentage difference or the percentage change formula is calculated when the difference between two values is divided by the average of the same values. We can say that the percentage difference is used to calculate the change in the value over the given period. Mathematically, we can be written as,

Percentage Difference = (Absolute difference / Average) × 100

Example: The Percentage difference between 50 and 100 will be:

= \dfrac{\left|50 - 100\right|}{\frac{50 + 100}{2}} \times 100
= 50/75 ×100
= 66.66%

Also Check:

• Percentage Increase Formula
• Percentage Decrease Formula
• Percentages – Aptitude Questions and Answers
• Problems on Percentage

Percentage Chart

Let's see the percentage chart of fractions converted into percentages.

Percentage Tricks

There are percentage tricks that can be used while calculating the percentage of numbers. The percentage trick below is the most used:

% x of y = % y of x

Let's solve 300% of 50.

Solution:

Here, solving 300% of 50 can be a little lengthy and tricky. However, using the trick it can be easily solved,

%x of y = %y of x
300% of 50 = 50% of 300
Now, solving 50% of 300 is relatively is. 50% of 300 is just half of 300. Therefore, 50% of 300 is 150.
Therefore, 300% of 50 is 150.

Related Articles:

• Tricks for Percentage
• Fractions
• Ratio and Proportions Formula

Solved Example of Percentage

Example 1: Find 15 % of 500.

Solution:

We can find the percentage by formula, 

V₂ = P × V₁
⇒ V₂ = 15% × 500
⇒ V₂ = (15 × 500) / 100 
⇒ V₂ = 75.

Thus, 15% of 500 is 75.

Example 2: What percentage is 1 of 3000?

Solution:

We can find the percentage by formula,

V₂ = P × V₁
⇒ P = V₂ / V₁
⇒ P = 1 / 3000

Thus, P% = 1/3000 × 100
⇒ P% = (1/30)%

Thus, 1 is 0.00333% of 3000.

Example 3: If 10% of x is 900. Find x.

Solution:

We can find the percentage by the formula,

V₂ = P × V₁
⇒ V₁ = V₂ / P
⇒ V₁ = (V₂ × 100 ) / P%
⇒ V₁ = (900 × 100) / 10
⇒ V₁ = 9000

Thus, the value of x is 9000.

Example 4: Find the value of the percentage of green blocks in each case.

Solution:

• In first case, the green blocks are 0, and the total blocks are 36. 
  Therefore, Percentage of green Blocks = 0/36 × 100 = 0%.

• In second case, the green blocks are 18, and the total blocks are 36. 
  Therefore, Percentage of green Blocks = 18/36 × 100 = 50%.

• In third case, the green blocks are 27 and the total bricks are 36. 
  Therefore, Percentage of green Blocks = 27/36 × 100 = 75%.

Suggested Quiz

10 Questions

Sudheer’s family can use the water up to 10 days when the tank is full. If the water consumption of his family is increased by 25% per day, how many days will the water tank last?

• A

  5

• B

  6

• C

  7

• D

  8

Explanation:

Let the water capacity of the tank be x liters.
Then, Initial water consumption rate = x/10 ltr per day
New water consumption rate after the increase by 25% = x/10 × (1 + 25/100) ltr per day = x/10 × 1.25 = x/8 ltr per day
The water tank last in number of days = full tank capacity in ltr / new water consumption rate in ltr per day = x / (x/8) = 8 days.

A product is sold at two consecutive discounts of 30% and subsequently 40%. If the marked price on the product is 1500, What is the selling price of the product?

• A

  420

• B

  360

• C

  600

• D

  630

Explanation:

SP = (70×1500/100)×(60/100) = 0.42×1500 = 630.

Jack and Robert appeared in an examination. Robert scored 9 marks less than Jack. Jack's score was 56% of the sum of their scores added together. Calculate their individual scores.

• A

  22 and 33

• B

  41 and 35

• C

  40 and 35

• D

  42 and 33

Explanation:

Let Robert's score be x. Then, Jack's score = x+9.
Now, x+9 = 56% of [(x+9) + x]
x+9 = 14/25 × (2x + 9)
25 × (x+9) = 14 × (2x+9)
25x + 225 = 28x + 126
3x = 99 ⇒ x = 33.
Therefore, Robert scored 33 marks and Jack scored 42 marks.

Mary buys an item at Rs 25 in a sale and saves Rs 5. Find out the percentage of her savings.

• A

  40/3 %

• B

  55/3 %

• C

  50/3 %

• D

  None of these

Explanation:

Original Price of the item = 25 + 5 = Rs 30.
Hence, the required percentage = (5/30) × 100% = 50/3 %.

Jack consumes 75% of his salary. Later his salary is increased by 20% and he increases his expenditures by 10%. Find the percentage increase in his savings.

• A

  51%

• B

  60%

• C

  50%

• D

  55%

Explanation:

Let Jack's original salary be Rs 100.
Then, his expenditure = Rs 75, his savings = Rs 25.
Now, his new salary = Rs 120.
So, new expenditure = (110/100) × 75 = Rs 165/2,
new savings = 120 - 165/2 = Rs 75/2.
Increase in savings = 75/2 - 25 = Rs 25/2.
Therefore, percentage increase in savings = (25/2)/25 × 100% = 50%.

The price of sugar is decreased by 10%. As a consequence, monthly sales is increased by 30%. Find out the percentage increase in monthly revenue.

• A

  17 %

• B

  19 %

• C

  18 %

• D

  None of these

Explanation:

Let the price of sugar be Rs 100 and monthly sales be 100 units.
Then, total revenue = 100 × 100 = Rs 10000.
And, new revenue = 90 × 130 = Rs 11700.
Increase in revenue = 11700 - 10000 = Rs 1700.
Hence, percentage increase in revenue = (1700/10000) × 100% = 17%.

John earns 33.33% more than Peter. By what percentage is Peter's earnings less than that of John's?

• A

  22 %

• B

  25 %

• C

  26 %

• D

  23 %

Explanation:

John earns 33.33% more than Peter ⇒ John = 133.33,

Peter = 100.
Difference = 33.33.

33.33/133.33×100=25%

Peter earns 25% less than John.

Barack spends Rs 6650 to buy some goods and gets a rebate of 6% on it. After this, he pays a sales tax of 10%. What is his total expenditure?

• A

  Rs 6870.10

• B

  Rs 6876.10

• C

  Rs 6865.10

• D

  Rs 6776.10

Explanation:

Rebate received by Barack = 6% of Rs 6650 = 6/100 × 6650 = 3/5 × 665 = Rs 399.
Sales Tax paid by Barack = 10% of Rs (6650-399) = 10% of Rs 6251 = Rs 625.10.
Therefore, Barack's total expenditure = Rs (6251 + 625.10) = Rs 6876.10.

By giving 5 more quiz test (passed 3 and failed 2) the passing percentage of the Viju changes from 80% to 75%. What is the total number of Quiz test he has given in total?

• A

  15

• B

  17

• C

  20

• D

  25

Explanation:

Let the quizes given be x. 
Therefore the quizes failed be 20% of x = x / 5. 
Given giving 5 more quizes and losing to the fail % becomes (100 - 75) = 25%. 
Therefore, (x + 5) * 25 / 100 = x / 5 + 2 x = 15 
Total number of quizes be 15 + 5 = 20

The price of a toy was decreased by 20% on some sale. and then the reduced price was increased by 20%. What is the change in price with respect to the initial price.

• A

  4% decrease

• B

  2% increase

• C

  remains same

• D

  10% increase

Explanation:

Let the initial price be 100. After 20% decrease the new price is 100 - 20 = 80 Now after 20% increase = 80 + 20 % of 80 = 96 The price change is 100 - 96 = 4 i.e. 4% decrease

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