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Percentage is referred to as a number or a ratio represented in the form of fractions of 100. We can represent percentage by using the ‘%’ symbol. In simple words, percentage is defined as how much of one quantity is made by another quantity and it is calculated in terms of 100. Percentage is a dimensionless quantity as if we say 40% of a number, then it means 60 percent of its whole. The percentage change is simply described as the increase and decrease in the final value of any number with a certain ratio or proportion.
Key Terms: Percentage, Percentage change, Percentage Increase. Percentage Decrease, Percentage Formula
Also Read: Math Formulas
Percentage Change
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Percentage change is mainly used for many purposes in finance, often to represent the price change of a stock over time, expressed as a percentage. It is used to compare the values of different currencies. In simple words, it is a derived value obtained by course of increase or decrease in the initially estimated value of something. The value obtained after the calculation is decided as the value of percentage change.
Percentage Change
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Percentage Increase Formula
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Percentage increase is the increase in the value of a number by a certain percent. It means that the value of an item has been increased by the initial value estimated in a definite period of time. It is calculated by using the percentage increase formula and the final number is obtained in percentage.
Percentage increase = [(Final value - Initial value) / Initial value] *100
The percentage increase formula can be easily derived in just two steps:
Step 1: Find the difference between final value and the initial value.
Increase Value = Final value - Initial value
Step 2: Divide the resultant value by initial value and then multiplying it by 100, to get the number in percent.
Percentage increase = [(Final value - Initial value) / Initial value] *100
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Percentage Decrease Formula
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Percentage decrease formula is used to reduce the quantity relative to its initial value. To find the percentage decrease, first, we need to calculate the difference in values. Then, dividing the difference by starting value and multiplying it by 100. Formula for percentage decrease is given:
Percentage decrease = [(Initial value - Final value) / Initial value] *100
The percentage decrease formula can be derived in three steps:
Step 1: Find the decreased value from the number,
Decreased value = Initial value - Final value
Step 2: Multiplying that value by 100. This makes the percentage decrease formula:
Percentage decrease = [(Initial value - Final value) / Initial value] *100
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Things to Remember
- Percentage calculation means finding the whole number in terms of 100.
- Percentage is described as the ratio or number for measuring the value ratio, where the value is always 100.
- The difference between the new and old values is expressed as percentage change.
- Percentage decrease denotes the percentage change in a value as it is lowered over time.
- Percentage increase formula has applications in various real-life activities such as comparing profits of a business, percentage increase of salary of any person, percentage increase in production of goods and many more.
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Sample Questions
Ques. A shopkeeper has to sell a pair of pens for Rs 25. He reduced the price of the same pair of pens to Rs 21. Calculate the percentage decrease in cost. (2 Marks)
Ans. The decreased amount = Rs (25-21) = Rs 4.
Hence, the decrease in percentage = (4/25) *100
decrease in percentage = 16%
Ques. A fruit seller needs to sell bananas for Rs 40 per dozen. He then reduced the cost of a dozen bananas by 10%. What will be the final price of a dozen bananas now? (2 Marks)
Ans. Let the new value of one dozen bananas is Rs x.
Decrease value = 40-x
According to percentage decrease formula,
Percentage decrease = (Decrease value / Old value) *100
10 = [(40-x) / 40] *100
10/100 = (40-x)/40
40-x = 4
x = 36
Therefore, the price of one dozen bananas is Rs 36.
Ques. The number 53 is misread as 35. Find the percentage decrease using the percentage decrease formula. (2 Marks)
Ans. New value = 35
Old value = 53
According to percentage decrease formula,
Percent decrease = [(Initial value - Final value) / Initial value] *100
Percent decrease = [(53-35)/53] *100
Percent decrease = (18/53) *100
Percent decrease = 33.9%
Hence, the percentage decrease is approximately 34%.
Ques. Mrs. Sudha had a 50% increase in her salary. If her final income was Rs 2000, what was her initial income? (3 Marks)
Ans. Final income is Rs 2000 and percentage increase is 50%
Let the initial income be x.
According to percentage increase formula,
Percentage increase = [(Initial value - Final 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. The cost of a membership card of a club was reduced by 20% and costs Rs 550 now. What will be the original price of the membership card before its cost was reduced? (3 Marks)
Ans. Let the original cost be x
Decrease value = x-550
According to percentage decrease formula,
20 = [(x-550)/x] *100
20/100 = (x-550)/x
5x-2750 = x
4x = 2750
x = 687.5
Therefore, the original price of membership card was Rs. 687.5
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? (3 Marks)
Ans. Initial amount is Rs 500 and percentage increase is 10%.
Let the final amount be x
So, by applying percentage increase formula,
10 = [(x-500)/500] *100
10/100 = [(x-500)/500]
0.1 = [(x-500)/500]
0.1*500 = x-500
50 = x-500
50+550 = x
x = 550
Therefore, the final amount that Manni had in her pocket after she came back from the bank is Rs. 550.
Ques. What will be the percentage change in the rent of the residence if it was Rs 20,000 in January and Rs 15,000 in March? (2 Marks)
Ans. From the question, we can say that rent has decreased.
Reduced value = 20,000 - 15,000
Reduced value = 5000
According to percentage decrease formula,
Percentage change = (Decrease value/Original value) *100
Percentage change = (5000/20000) *100
Percentage change = 25%
Therefore, the rent has been reduced to 25%.
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