General terms related to spherical mirrors: A mirror with the shape of a portion cut out of a spherical surface or substance is known as a...

General Terms Related to Spherical Mirrors

April 11, 2024**Percentage Increase Formula: **Percentage is a fraction with denominator \(100,\) represented with the symbol \(\% .\) We have been using the percentage in comparing the results. Many times, we need to know the increase or decrease in a certain quantity as a percentage. For example, the increase in a city’s population can be understood better if we say the population increased by \(10\% .\) This article will discuss percentages and the formula to find the percentage increase.

Per means out of, cent means hundred. Therefore, per cent means out of every hundred. The percentage is a fraction with a denominator of \(100.\) The word percentage comes from the Latin word per centum, which means “one hundred.”

The symbol \(\% \) represents the percentage.

We frequently see percentage statistics in newspaper articles, television news, and other facets of our lives. Percentage computations are extensively used in the business to compute interest rates, costs, and profits etc.

**Example:** “Sophia got \(72\) per cent marks in English” means that she got \(72\) marks out of \(100.\)

**Learn All the Concepts on Percent Change**

To convert a fraction into a percentage, we multiply the fraction by \(100.\)

Example: Express \(\frac{1}{2}\) as a percentage.

So, \(\frac{1}{2}\) as a percentage \( = \frac{1}{2} \times 100 = 50\% \)

To convert a ratio into a percentage, first change it to a fraction and then multiply it by \(100.\)

**Example:** Express \(3:4\) as a fraction.

The given ratio \(3:4\) in the fraction is \(3:4 = \frac{3}{4}.\)

Now, the fraction \(\frac{3}{4}\) in percentage \( = \frac{3}{4} \times 100\% = 75\% .\)

To convert a decimal to a percentage, multiply it by \(100\) or shift the decimal point two places to the right and write the answer with a per cent sign \(\% \) next to it.

Example: Convert \(0.65\) to the percentage.

So, we have \(0.65 = 0.65 \times 100\% = 65\% \)

To convert a percentage into a fraction, divide the percentage by \(100.\)

Example: Convert \(25\% \) to fractions.

Hence, we have, \(25\% = \frac{{25}}{{100}} = \frac{1}{4}.\)

We now understand that the \(\% \) stands for “per \(100\)”. A hundred per cent of something can be said to be the entire item. The increase or decrease in the original value is expressed as a percentage change. If the current value is greater than the beginning value, the percentage increase can be calculated.

If the current number is smaller than the previous value, the percentage decline can determine how much it has fallen.

When a value is reduced by a certain percentage over a period of time, it is referred to as a percentage decrease.

Examples: A drop in rainfall, a drop in the number of Covid patients, and so on.

The per cent decrease formula can be used to determine the per cent decrease.

The percentage decrease formula can figure out how much the decreased value differs from the beginning value. The percentage decrease formula is the ratio of a quantity’s decrease over its initial value multiplied by \(100\) and given as a percentage.

The formula to find the percentage decrease is given by:

Percentage decrease \( = \frac{{{\rm{amount}}\,{\rm{of}}\,{\rm{decrease}}}}{{{\rm{original}}\,{\rm{amount}}\,{\rm{or}}\,{\rm{base}}}} \times 100\% ,\)

where the amount of decrease \( = {\rm{Original}}\,{\rm{value}} – {\rm{New}}\,{\rm{value}}.\)

Depending on the new and old values, it could represent a per cent increase or decrease. The outcome will be positive if the new value is greater than the old value, and we will have an increase. If the new value is less than the old value, the outcome will be negative, and we will have a drop.

Now, in the case of an increase, the difference after subtracting the original value from the increased value, dividing by the original value, and then multiplied by \(100\) gives us the percentage increase of the given value.

The percentage increase formula can be figured out by how much percentage the increased value differs from the beginning value. The percentage increase formula is the ratio of a quantity’s increase over its initial value multiplied by \(100\) and given as a percentage.

The formula to find the percentage increase is given by:

Percentage increase \( = \frac{{{\rm{amount}}\,{\rm{of}}\,{\rm{decrease}}}}{{{\rm{original}}\,{\rm{amount}}\,{\rm{or}}\,{\rm{base}}}} \times 100\% ,\)

where amount of increase \( = {\rm{New}}\,{\rm{value}} – {\rm{Original}}\,{\rm{value}}.\)

Steps to calculate the percentage increase are,

1. First, calculate the difference (increase) between the two numbers being compared.

2. \({\rm{Increase}} = {\rm{new}}\,{\rm{number}} – {\rm{original}}\,{\rm{number}}\)

3. Then multiply the result by \(100\) by dividing the increase by the original amount.

4. \({\rm{Percentage}}\,{\rm{increase}} = \frac{{{\rm{Increased}}\,{\rm{value}}}}{{{\rm{Original}}\,{\rm{value}}}} \times 100\% \)

**What is the per cent of change from 5 to 9?**

From the given information, we get, initial value \( = 5,\) Increased value \( = 9 – 5 = 4.\)

The percentage increase formula is given by:

\({\rm{Percentage}}\,{\rm{increase}} = \frac{{{\rm{Increased}}\,{\rm{value}}}}{{{\rm{Original}}\,{\rm{value}}}} \times 100\)

\( \Rightarrow {\rm{Percentage}}\,{\rm{increase}} = \frac{4}{5} \times 100\)

\( \Rightarrow {\rm{Percentage}}\,{\rm{increase}} = 80\% \)

Hence, \(80\% \) is per cent of change from \(5\) to \(9.\)

Some of the uses of the percentage increase/decrease formula are listed below:

1. The use of percentages is beneficial for examining or comparing results and progress. When the base condition for comparison is modified, the percentage increase/ decrease formula becomes much more helpful.

2. These formulas help compare the population of a city or country and get the exact increased or decreased percentage of the city or country population.

3. The percentage increase/decrease formula helps a lot in schools, colleges to compare the students’ results.

**Learn How to Calculate Percentage?**

** Q.1. A school team won 10 games this year against 8 games won last year. What is the per cent increase?** Increased wons \( = 10 – 8 = 2\)

Ans:

The formula to find the percentage increase is given by,

\({\rm{Percentage}}\,{\rm{increase}} = \frac{{{\rm{amount}}\,{\rm{of}}\,{\rm{increase}}}}{{{\rm{original}}\,{\rm{amount}}\,{\rm{or}}\,{\rm{base}}}} \times 100\)

\({\rm{Percentage}}\,{\rm{increase}} = \frac{{{\rm{increase}}\,{\rm{in}}\,{\rm{the}}\,{\rm{number}}\,{\rm{of}}\,{\rm{wins}}}}{{{\rm{the original}}\,{\rm{number}}\,{\rm{of}}\,{\rm{wins}}}} \times 100\)

\({\rm{Percentage}}\,{\rm{increase}} = \frac{2}{8} \times 100\)

\({\rm{Percentage}}\,{\rm{increase}} = 25\% \)

Therefore, \(25\% \) is obtained.

** Q.2. My mother says, in her childhood petrol was Rs 10 a litre. It is Rs 100 per litre today. By what percentage has the price goes up?** From the given information, initial value \( = {\rm{Rs}}\,10,\) New value \( = {\rm{Rs}}\,100\)

Ans:

Increased price \( = {\rm{Rs}}\,100 – 10 = {\rm{Rs}}\,90\)

Percentage increase \( = \frac{{{\rm{amount}}\,{\rm{of}}\,{\rm{increase}}}}{{{\rm{the}}\,{\rm{original}}\,{\rm{price}}}} \times 100\% \)

\( = \frac{{90}}{{10}} \times 100 = 900\% \)

Therefore, \(900\% \) is the increase in the percentage of the petrol price.

** Q.3. What is the percentage change in the rent of the house if in the month of January it was Rs. 20,000 and in the month of March it is Rs. 22,000?** From the given information, initial rent \( = {\rm{Rs}}\,20000,\) New rent \( = {\rm{Rs}}\,22000\)

Ans:

Increase in rent \( = {\rm{Rs}}\,22000 – {\rm{Rs}}\,20000 = {\rm{Rs}}\,2000\)

Hence, the percentage increase in rent \( = \frac{{{\rm{amount}}\,{\rm{of}}\,{\rm{increase}}}}{{{\rm{the}}\,{\rm{original}}\,{\rm{rent}}}} \times 100\% = \frac{{2000}}{{20000}} \times 100 = 10\% \)

Therefore, \(10\% \) is the increase of the rent in percentage.

** Q.4. Arun bought a car for Rs 4,50,000. The next year, the price went upto Rs 4,68,000. What was the percentage of the price increase?**From the given information, initial price of the car \( = {\rm{Rs}}\,450000,\) new price of the car \( = {\rm{Rs}}\,468000\)

Ans:

Increase in price of the car \( = {\rm{Rs}}\,468000 – {\rm{Rs}}\,450000 = {\rm{Rs}}\,18000\)

Hence, the percentage increase in rent \( = \frac{{{\rm{amount}}\,{\rm{of}}\,{\rm{increase \,in\, price}}}}{{{\rm{the}}\,{\rm{original}}\,{\rm{price}}}} \times 100\% = \frac{{18000}}{{450000}} \times 100 = 4\% \)

Therefore, \(4\% \) is the increase of the car price in percentage.

** Q.5. The population of the city increased from 40,000 to 50,000. Find the percentage increase.**From the given information, initial polulation \( = 40000,\) final population \( = 50000\)

Ans:

Increase in polulation \( = 50000 – 40000 = 10000\)

Hence, the percentage increase in population \( = \frac{{{\rm{amount}}\,{\rm{of}}\,{\rm{increase\, in\, population}}}}{{{\rm{the}}\,{\rm{original}}\,{\rm{population}}}} \times 100\% \)

\( = \frac{{10000}}{{50000}} \times 100 = 20\% \)

Therefore, \(20\% \) is the increase in the population of the city.

The difference after subtracting the original value from the increased value, dividing by the original value, then multiplying the final result by \(100\) is known as a percentage increase. This article includes the definition of percentage, percentage increase, percentage increase formula, and examples.

This article helps in better understanding the topic percentage increase formula. This article’s outcome helps in applying the suitable formulas while solving the various problems based on them.

** Q.1. What is the formula for calculating percentage increase?** The formula to find the percentage increase is given by:

Ans:

Percentage increase \( = \frac{{{\rm{amount}}\,{\rm{of}}\,{\rm{increase}}}}{{{\rm{original}}\,{\rm{amount}}\,{\rm{or}}\,{\rm{base}}}} \times 100\% \)

** Q.2. What is the percentage formula?** To compute a percentage, divide the part of the value by the entire amount and multiply the result by \(100.\)

Ans:

The formula for calculating percentages is

\( = \frac{{{\rm{part}}\,{\rm{of}}\,{\rm{the}}\,{\rm{value}}}}{{{\rm{the}}\,{\rm{total}}\,{\rm{value}}}} \times 100\% .\)

** Q.3. How do you calculate a 5% increase?** To calculate a \(5\% \) increase, we consider the following example.

Ans:

The original cost of the shirt is \({\rm{Rs}}\,500,\) later the price of the shirt is increased by \(5\% \) by the shopkeeper. Then find the increased cost of the shirt.

\(5\% \) of \(500 = \frac{5}{{100}} \times 500 = {\rm{Rs}}\,25\)

Hence, the increase in the price of the shirt \( = {\rm{Rs}}\,25\)

So, the new cost of the shirt is \({\rm{Rs}}\,500 + {\rm{Rs}}\,25 = {\rm{Rs}}\,525.\)

** Q.4. What is an example of use of percentage increase formula?** An example of the use of the percentage increase formula is given by the following example.

Ans:

The original cost of a brand of a TV set is \({\rm{Rs}}\,15000,\) later the price of the TV set is increased to \({\rm{Rs}}\,18000\)

In this case, the increase in the price of the TV set is \( = {\rm{Rs}}\,18000 – {\rm{Rs}}\,15000 = {\rm{Rs}}\,3000.\)

So, the percentage increase in the price of the TV set \( = \frac{{{\rm{the}}\,{\rm{increased}}\,{\rm{value}}}}{{{\rm{the}}\,{\rm{original}}\,{\rm{value}}}} \times 100\% \)

\( = \frac{{3000}}{{15000}} \times 100\% = 20\% .\)

** Q.5. How do you calculate percentage increase manually?**Steps to calculate the percentage increase manually are:

Ans:

1. To begin, calculate the difference (increase) between the two numbers being compared.

2. \({\rm{Increase}} = {\rm{the}}\,{\rm{new}}\,{\rm{number}} – {\rm{the}}\,{\rm{original}}\,{\rm{number}}\)

3. Then multiply the result by \(100\) by dividing the increase by the original amount.

4. \({\rm{Percentage}}\,{\rm{increase}} = \frac{{{\rm{the}}\,{\rm{increased}}\,{\rm{value}}}}{{{\rm{the}}\,{\rm{original}}\,{\rm{value}}}} \times 100.\)