Percentage Decrease Formula: The percent decrease formula helps us find how much percentage a variable has decreased in its value. The term percentage is derived from the Latin word per centum, meaning per hundred. \(\% \) is the symbol for percentage. We often come across percentage figures in newspaper reports, news on television, and other aspects of our life. In the finance industry, percentage computations are commonly used to calculate interest rates, costs, prices, profits, etc. Also, we often compare economic data using percentages.

In this article, we will discuss percentages and learn to find the formula to find the percentage decrease.

What is Percentage in Math?

Per means ‘for every’ or ‘out of’ and cent means ‘hundred’. Thus, percent means for every hundred or out of hundred.

If in an examination for \(100\) marks, Jyoti scored \(83\) marks, that means Jyoti scored \(83\) percent marks. Conversely, if in the same examination, Manu secured \(67\) percent marks, that means Manu has got \(67\) marks out of \(100\).

The symbol for percent is \(\%\). Thus, the percent is the numerator of a fraction with a denominator of \(100\).
For example, \(40\) out of \(100=\frac{40}{100}=40\) as percent, written as \(40\, \%\).

Thus, when a fraction is expressed with denominator \(100\), the corresponding numerator is called percent or percentage.

Hence, \(\frac{15}{100}=100\, \%, \frac{2}{100}=2\, \%\), and so on.

We do not follow any difference between percent and percentage strictly. Before we learn about the formula for percentage decrease, let us first look at the basic conversions like converting fractions and decimals into percentages, converting percentages into fractions and decimals, etc.

Converting Fractions and Decimals Into Percentage

Multiply the given fraction or decimal by \(100\) and at the same time write the sign of percentage. To speak plainly, to convert a fraction into a percentage, write the given fraction as an equivalent fraction with denominator \(100\).

For example, \(\frac{3}{4}=\frac{3}{4} \times 100\, \%=75 \,\%, \frac{7}{20}=\frac{7 \times 5}{20 \times 5}=\frac{35}{100}=35 \,\%\),

\(0.224=0.224 \times 100\, \%=22.4 \,\%\).

Converting Percentage Into Fractions and Decimals

To convert percentage into fraction, remove the sign of the percentage and at the same time divide by \(100\). Then reduce the resulting fraction obtained to its lowest terms or decimal as required. In simple, to convert percentage into a decimal, remove the \(\%\) symbol and divide by \(100\)

For example, \(2.5 \,\%=\frac{2.5}{100}=0.025\). We can write it as a fraction, i.e., \(\frac{25}{1000}=\frac{1}{40}\).

Expressing One Quantity as a Percentage of Another

A percentage can be used to compare a part to the whole or to compare two quantities. Divide the first quantity by the second one and at the same time multiply the result by \(100\, \%\). Let us study its application in the given examples.

Example 1: Express \(20 \mathrm{~kg}\) as a percentage of \(200 \mathrm{~kg}\).
Solution: \(\frac{20}{200} \times 100\, \%=10\, \%\)

Example 2: There are \(96\) students in a class, and \(54\) of them are girls. Find the percentage of girls in the class.
Solution: Percentage of girls in the class \(=\frac{54}{96} \times 100 \,\%\).
\(=56.25 \,\%\)

Percentage Change

We now know that the percentage indicates per \(100\). \(100\,\% \) of something can be said the whole of a thing. Percentage change means the increase or decrease in the original value. If the present value is more than the initial value, then the percentage increase can be determined by its increased value.

If the current value is less than the earlier value, then how much it has been decreased can be determined by the percentage decrease.

Percentage Increase or Decrease

The above scenario shows that quantities such as the country’s population and its water supply can increase or decrease over time. The required percentage increase in water supply will depend on the percentage increase in the country’s population, among other factors. We can compare the extent of change in quantities as a percentage increase or decrease.

Percentage Decrease

A percentage decrease measures the percentage of decline in the value of a quantity from its original value. Therefore, to calculate a percentage decrease, we have to know the reduction in the value of an amount from its initial value. The new value is called the decreased value.

Percentage Decrease Formula

A decrease in percentage refers to the percentage change in the value that has been decreased over a while. 
Percentage decrease can be computed by using the following formula:

Decrease \(=\) Original value \(-\) Decreased value
Percentage Decrease \(=\frac{\text { Original value-Final value }}{\text { Original value }} \times 100\, \%\)
Percentage decrease \(=\frac{\text { Decrease }}{\text { Original value }} \times 100 \,\%\)
Decreased value \(=(100 \,\%-\) Decrease \(\%) \times\) Original value,
where decrease \(\%\) means percentage decrease. The examples of decrease percentages in real life are a decrease in employment, a discount on the marked price of a quantity, a loss percentage of a quantity, etc.

Percentage Decrease Formula Examples

Example 1 : The price of coffee decreases from \(₹\, 40\) per \(\mathrm{kg}\) to \(₹ \,32\) per \(\mathrm{kg}\). Find the decrease in percentage.
Solution: If the price of coffee falls from \(₹ \,40\) per \(\mathrm{kg}\) to \(₹ \,32\) per \(\mathrm{kg}\), then
Reduction in price \(=₹\, 40-₹ \,32=₹\, 8\)
Therefore, decrease \(\%=\frac{\text { Decrease in price }}{\text { Original price }} \times 100\, \%=\frac{8}{40} \times 100\, \%=20\, \%\)

Example 2: Varun has \(3\) times as much saving as Gunjan. He spends \(40\,\%\) of his saving on buying a pair of sports shoes. By what percentage must Gunjan increase her savings to make her and Varun’s remaining savings the same?
Solution: Let \(₹\, x\) be the original saving of Gunjan and let \(y \,\%\) be the percentage increase of her savings.
Gunjan’s savings after increase \(=\) Varun’s saving after spending
Thus,
\(x \times(100\, \%+y \,\%)=3 x \times(100\, \%-40\, \%)\)
\(100 \,\%+y \,\%=180 \,\%\)
\(y \,\%=80 \,\%\)
Hence, the required percentage increase of Gunjan’s savings is \(80\, \%\).

Example 3: Most of the water on earth is salty. Only \(2.7\, \%\) of the available water is fresh. Find the percentage of water that is unfit for drinking and out of \(1,00,000 \mathrm{~m}^{3}\) of water, what amount of water is fit for drinking?
Solution: Since \(2.7\, \%\) of the available water is fit for drinking,
Therefore, the water unfit for drinking \(=100\, \%-2.7 \,\%=97.3 \,\%\)
Also, the quantity of water fit for drinking \(=2.7 \,\%\) of the water taken
\(=\frac{2.7}{100} \times 1,00,000=2,700 \mathrm{~m}^{3}\)

Solved Examples – Percentage Decrease Formula

Q.1. Preethu’s weight decreased from \(140 \mathrm{~kg}\) to \(133 \mathrm{~kg}\). Find the percentage decrease in her weight.
Ans: Decrease in Preethu’s weight \(=140-133=7 \mathrm{~kg}\)
Percentage decrease in weight \(=\frac{\text { Decrease }}{\text { Original value }} \times 100\, \%\)
\(=\frac{7}{140} \times 100 \,\%\)
\(=5 \,\%\)
Hence, the percentage decrease in her weight is \(5 \,\%\).

Q.2. The cost of an article is decreased from \(15 \,\%\). If the original price is \(₹\, 80\), find the reduced cost.
Ans: The original cost \(=₹\, 80\)
Decrease in cost \(=15\,\%\) of \(₹\, 80=\frac{15}{100} \times 80=₹\, 12\)
Therefore, decreased cost \(=₹\, 80-₹\, 12=₹ \,68\)

Q.3. The length of a pair of trousers is assumed to shrink by \(4\, \%\) after its first wash. If Manu wants to buy a pair of trousers that is \(102 \mathrm{~cm}\) long after the first wash, how long should the pair of trousers be?
Ans: Let \(y \mathrm{~cm}\) be the length of the pair of trousers that Manu should buy.
Length of trouser after shrinkage \(=(100 \,\%-\) Decrease \(\,\%) \times\) Original value
\(102=(100 \,\%-4\, \%) \times x\)
\(102=\frac{96}{100} x\)
\(x=\frac{102}{.96}=106.25\)
Hence, the pair of trousers should be \(106.25 \mathrm{~cm}\) long.

Q.4. The volume of an ice cube is \(150 \mathrm{~cm}^{3}\). Its volume decreased by \(23\, \%\) after an hour. Find the volume of the remaining ice.
Ans: Volume of the remaining ice \(=(100\, \%-\) Decrease \(\,\%) \times\) Original value
\(=(100\, \%-23 \,\%) \times 150=\frac{77}{100} \times 150\)
\(=115.5 \mathrm{~cm}^{3}\)
Hence, the volume of the remaining ice is \(115.5 \mathrm{~cm}^{3}\).

Q.5. Out of \(₹ \,36,000\), two-fifth were kept in a bank. Of the remaining money, \(40\, \%\) is spent on food and \(15\, \%\) on rent. Find out how much money is spent on food and how much on rent?
Ans: Money kept in bank \(=\frac{2}{5} \times ₹ \,36,000=₹ \,14,400\)
Thus, the remaining money \(=₹\, 36,600-₹ \,14,400=₹\, 21,600\)
Now, money spent on food \(=40 \,\%\) of \(₹\, 21,600\)
\(=\frac{40}{100} \times ₹\, 21,600=₹\, 8,600\)
And, money spent on rent \(=15 \,\%\) of \(₹ \,21,600\)
\(=\frac{15}{100} \times ₹ \,21,600=₹\, 3,240\)

Summary

In this article, we learned and discussed the percentage decrease formula and the basic concept related to percent before that. We discussed converting fractions and decimals into a percentage, converting percentages into fractions and decimals. Then, later we did a detailed discussion about the percentage decrease formula and mastered ourselves after solving a handful of examples based on the percentage decrease formula.

Frequently Asked Question – Percentage Decrease Formula

Q.1. What is the percentage increase/decrease formula
Ans: Percentage increase \(=\frac{\text { Increase }}{\text { Original value }} \times 100 \,\%\)
And percentage decrease \(=\frac{\text { Decrease }}{\text { Original value }} \times 100 \,\%\)

Q.2. Define percentage decrease.
Ans: A percentage decrease measures the reduction in the value of a quantity from its initial value. Therefore, to calculate a percentage decrease, we have to know the decline in the value of an amount from its original value. The new value is called the decreased value.

Q.3. Define percent.
Ans: Percent means for every hundred or out of hundred. The symbol for percent is \(\%\). Therefore, the percent is the numerator of a fraction with a denominator \(100\).
For example, \(80\) out of \(100=\frac{80}{100}=80\) as percent, written as \(80\, \%\).
Thus, when a fraction is expressed with its denominator is \(100\), the corresponding numerator is called percent or percentage.

Q.4. What is the percentage decrease formula?
Ans: A decrease in percentage refers to the percentage change in the value decreased over a while. 
Percentage decrease can be computed by using the following formula:
Decrease \(=\) Original value \(-\) Decreased value
Percentage decrease \(=\frac{\text { Decrease }}{\text { Original value }} \times 100 \,\%\)
Decreased value \(=(100 \,\%-\) Decrease \(\%) \times\) Original value
where decrease \(\%\) means percentage decrease.

Q.5. What is the percent change of \(50\) to \(35\)?
Ans: Since \(50\) is decreased to \(35\),
The final value \(=35\)
The original value \(=50\)
We know that, percentage decrease \(=\frac{\text { Original value-Final value }}{\text { Original value }} \times 100 \,\%\)
Thus, the percentage change \(=\frac{50-35}{50} \times 100 \,\%=\frac{15}{50} \times 100 \,\% \Rightarrow \frac{3}{10} \times 100 \,\%=30\, \%\).
Hence, the percent change or the percentage decrease from \(50\) to \(35\) is \(30\, \%\).

We hope this detailed article on the percentage decrease formula helped you in your studies. If you have any doubts or queries regarding this topic, feel to ask us in the comment section and we will be more than happy to assist you.