Education Journalist | Study Abroad Lead
Percentage increase is referred to as the share of the percentage of something in terms of 100%. As we know, Percentage is used in our everyday life activities to compare quantities by 100. The percentage is any number that is ‘by the hundred’ or ‘divide by one hundred’. When we say 100% of something, it, therefore, means the whole of it. Using percentages makes it far more convenient for us to measure things. The percentage increase formula is a term used to find the share percentage of something in terms of 100% or whole. It is a very significant mathematical term that helps in the comparison of quantities in a simplified way. With this formula, it becomes a lot easier to calculate profit growths, increase in market rates, salary, or even exam marks. In this chapter, we shall learn all about the percentage increase formula including its definition, way of usage, and applications in daily life.
| Table of Content |
Key terms: Percentage, percentage increase formula, Percentage calculation, equivalent ratios
What is Percentage Increase Formula?
[Click Here for Sample Questions]
The percentage increase formula is the formula used to compare growth in a quantity from its initial to final value over a given period of time. The formula is mathematically represented as the difference between the final and the initial value which is further divided by the initial value and multiplied by 100.
Percentage increase can be more specifically defined as the difference between the final and initial value expressed in the form of a percentage. We need to first have the initial and final values of an object and using this concept, we can calculate percentage increase by the following formula:
Percentage Increase = [ ( Final Value – Initial Value ) / Initial Value ] x 100
It is to be noted that the absolute value is to be taken for the initial value as a percentage should be a positive quantity.
Also read: Real numbers
How to Calculate Percentage Increase Formula?
[Click Here for Sample Questions]
Percentage increase can be more specifically defined as the difference between the final and initial value expressed in the form of a percentage. We need to first have the initial and final values of an object and using this concept, we can calculate percentage increase by the following formula:
Percentage Increase = [ ( Final Value – Initial Value ) / Initial Value ] x 100
It is to be noted that the absolute value is to be taken for initial value as a percentage should be a positive quantity.
Also Read: Area of square using diagonal
Uses of Percentage Increase Formula
[Click Here for Sample Questions]
The percentage increase formula is used all around us in various activities. It is helpful in comparing growth rates of values over time. Some real-life applications of the percentage formula include comparing profits of a business made over the years, in the percentage increase of someone’s salary, in the percentage increase in productions of goods made in a company, and many more. It helps us in understanding how much difference it has made in the quantity from the initial value to the final value expressed in percentage form.
For example, We have to calculate the percentage increase in the rent of a house. Let us consider in January the rent was Rs. 10,000 and in March the rent is Rs. 15,000.
To calculate the percentage increase, we have to first calculate the increase in the amount of rent,
15,000 - 10,000 = Rs. 5,000
Rent in January = Rs.10,000
Therefore, percentage increase = (5000 / 10000) * 100
= 50%
Also Read: Commutative property formula
Things to Remember
- The percentage is a mathematical medium used to compare quantities by 100.
- The percentage increase formula is the formula used to find the difference between the final and initial value expressed in the form of a percentage.
- The formula is mathematically represented as the difference between the final and the initial value which is further divided by the initial value and multiplied by 100.
- The percentage increase formula finds application in various real-life activities such as comparing profits of a business made over the years, in the percentage increase of someone’s salary, in the percentage increase in productions of goods made in a company, and many more.
Sample Questions
Ques. The rent of a house in January was Rs. 1000 and in March it has increased to Rs. 15000. Finds the percentage increase in the rent of the house. [3 marks]
Ans As we see, the initial rent is Rs. 1000 and the final rent is Rs. 15000. Therefore, applying the percentage increase formula, the increase in percentage is:
Percentage Increase = (Increased Value ⁄ Original Value) × 100
= (5000 ⁄ 10000) × 100
= 50%
Therefore, there is a 50% increase in the rent value.
Ques. The price of Riya’s chocolate has increased from Rs. 15 to Rs. 20. What is the percentage increase in the price of chocolate? [3 marks]
Ans As we see, the initial price is Rs. 15 and the final price is Rs. 20. Therefore, applying the percentage increase formula, the increase in percentage is:
Percentage increase = [(Final Value - Initial Value)/Initial Value] × 100.
= [(20 - 15) /15] × 100
= (5 /15) × 100
= 33.33%
Therefore, there is a 33.33% increase in the price.
Ques. If Mr. Sadhu had made a profit of Rs. 200 in December and it increased to Rs. 250 in February, find the percentage increase in his profits using the percentage increase formula. [3 marks]
Ans As we see, the initial profit is Rs. 200 and the final profit is Rs. 250. Therefore, applying the percentage increase formula, the increase in percentage is:
Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100.
= [(250 – 200) / 200] × 100
= (50 /2 00) × 100
= 25%
Therefore, there is a 25% increase in the profit.
Ques. Shalini made Rs. 2000 profit on her small business and within one month the profit went up to Rs. 3000. Find the percentage increase in Shalini’s profit. [3 marks]
Ans As we see, Shalini’s initial profit is Rs. 2000 and her final profit is Rs. 3000. Therefore, applying the percentage increase formula, the increase in percentage is:
Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100.
= [(3000 - 2000) / 2000] × 100
= (1000 / 2000) × 100
= 50%
Therefore, there is a 50% increase in the profit.
Ques. The price of a Hot Wheels car has increased from 15 Dollars to 20 Dollars. What is the percentage increase in the price of the car? [3 marks]
Ans As we see, the initial price of the Hot Wheels car is 15 dollars and the final price is 20 dollars. Therefore, applying the percentage increase formula, the increase in percentage is:
Percentage increase = [(Final Value - Initial Value)/Initial Value] × 100.
= [(20 - 15) / 15] × 100
= (5 /15) × 100
= 33.33%
Therefore, there is a 33.33% increase in the price of the Hot Wheels car.
Ques. Robin had scored 80 marks in Maths in the last term. However, his scores increased by 10 in the annual term. Applying the percentage increase formula, find out the percentage increase in Robin’s annual marks. [3 marks]
Ans As we see, Robin’s initial marks were 80 and his annual terms marks is 80 + 10 = 90. Therefore, applying the percentage increase formula, the increase in percentage is:
Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100.
= [(90 - 80) / 90] × 100
= (10/90) × 100
= 11.11%
Therefore, there is an 11.11% increase in Robin’s annual term marks in Maths.
Ques. Mrs. Sudha had a 50% increase in her salary. If her final income was Rs. 2000, what was her initial income? [5 marks]
Ans As we see, the final income is Rs. 2000 and the percentage increase is 50%.
Let us assume the initial income is X.
Therefore, applying the percentage increase formula,
Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100.
50 = [(2000 - x) / x] × 100
50 / 100 = (2000 – x) / x
0.5 = (2000 – x) / x
0.5x = 2000 - x
0.5x + x = 2000
1.5x = 2000
x = 2000 / 1.5
x = 1333.33
Therefore, Mrs. Sudha’s initial salary was Rs. 1333.33.
Ques. If Rahul has increased his tuition fees from Rs. 2000 to Rs. 3000, find the percentage increase in Shalini’s profit. [3 marks]
Ans As we see, Rahul’s initial fees are Rs. 2000 and his final fees are Rs. 3000. Therefore, applying the percentage increase formula, the increase in percentage is:
Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100.
= [(3000 - 2000) / 2000] × 100
= (1000 / 2000) × 100
= 50%
Therefore, there is a 50% increase in Rahul’s tuition fees.
Ques. The price of toffees has increased from Rs. 15 to Rs. 20. What is the percentage increase in the price of these toffees? [5 marks]
Ans As we see, the initial price of the toffees is Rs. 15 and the final price is Rs. 20. Therefore, applying the percentage increase formula, the increase in percentage is:
Percentage increase = [(Final Value - Initial Value)/Initial Value] × 100.
= [(20 - 15) /15] × 100
= (5 /15) × 100
= 33.33%
Therefore, there is a 33.33% increase in the price of the toffees.
Ques. Manni had Rs. 500 in her pocket when she left home for the bank. If the percentage increase in Manni’s money after she returned home is 10%, what was the final amount that Manni had in her pocket? [5 marks]
Ans As we see, the initial amount is Rs. 500, and the percentage increase is 10%.
Let us assume the final amount is X.
Therefore, applying the percentage increase formula,
Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100.
10 = [(X – 500) / 500] × 100
10 / 100 = [(X – 500) / 500]
0.1 = [(X – 500) / 500]
0.1 x 500 = X – 500
50 = X – 500
50 + 500 = X
Therefore, X = 550
So, the final amount that Manni had in her pocket after she came from the bank is Rs. 550.
Also Read:
Comments