Y is P% of X

Solution:

# Percentage Calculator

## What is a Percentage Calculator?

Percentage Calculator helps you in solving your percentage queries in a jiffy, along with an explanation describing the proper method or way to solve it, on your own.

Percentage problems include various formulas, the most common being X/Y = Px100.

## How to use this Percentage Calculator tool?

This percentage calculator tool is the easiest to use. Select the formula or percentage value you need to find out from the drop down. Then fill in the values asked. For instance, in the formula for ‘Y is P% of What?’, fill in the values for Y and P%, as required and click Calculate. Once you click ‘Calculate’, you get the final result with a detailed description of the solution. This helps you understand the complete calculation and correct implication of the formula.

## What is a percentage?

Just like ratios and fractions, percentage is also a way to express the relation of two numbers.

Percentages are widely used as they easily describe situations that include large numbers (like, chances of winning a lottery), average numbers (like, calculating your final grade), and small numbers (like determining the parts per million - PPM of NO2 in the air).

Generally, % sign is used as a percent sign, however, sometimes pct is also used to denote a percentage value. Whenever one wishes to know how much a number is bigger in relation to the other, percentages come into existence. Let’s take an example here.

For instance, if you want to calculate 30% of 20. It simply means to determine the 30 hundredths of 20. Mathematically, 30/100 * 20 = 6. With our percentage calculator tool, you can work with these percentages and decimal fractions with ease.

### How to find the percentage

There are a few different ways to find the percentage of a number, depending on the information you have.

To find the percentage of a number, you can use the formula: (part/whole) * 100

1. For example, if you have 10 apples and you want to know what percentage of the apples are red, and 2 of them are red, you can use the formula: (2/10) * 100 = 20%. This means that 20% of the apples are red.

To find the percentage of a number, you can also use the formula: (part/whole) * 100 = percentage

1. For example, if you have \$1000 and you want to know what percentage of the money you have saved, and you saved \$200, you can use the formula: (200/1000) * 100 = 20%. This means that you saved 20% of the money.

To find the percentage increase or decrease, you can use the formula: ((new value - old value) / old value) * 100

1. For example, if the price of a product was \$100 and it increased to \$125, you can use the formula: ((125-100) / 100) * 100 = 25%. This means that the price of the product increased by 25%.

To find the percentage of a number, you can also use the formula: (part/whole) * 100 = percentage

1. For example, if you have 1000 chocolates, and you want to know what percentage of the chocolates are dark chocolates, and you have 200 dark chocolates. you can use the formula: (200/1000) * 100 = 20%. This means that 20% of the chocolates are dark chocolates.

## How to figure out Percentages

There are various formulas to calculate percent values or related.

Here are some of the important formulas to determine the values and solve your queries.

### Type 1 - Y = P% * X

The formula Y = P% * X

can be used to calculate the percentage of a number X.

P is the percentage expressed as a decimal (e.g. 25% is 0.25) and Y is the result of the calculation.

Example 1:

If X = 100 and P% = 25,

then Y = X * P% = 100 * 0.25 = 25

This means that 25% of 100 is 25.

Example 2:

If X = 500 and P% = 10,

then Y = X * P% = 500 * 0.1 = 50

This means that 10% of 500 is 50.

Example 3:

If X = 1000 and P% = 5, then Y = X * P% = 1000 * 0.05 = 50

This means that 5% of 1000 is 50.

### Examples of Questions using Y = X * P%

Q1. A store is offering a 20% discount on all items. If a customer wants to buy a dress that costs \$100, how much will the customer pay after the discount?

Solution:

Let X = 100 (cost of the dress) and P% = 0.20 (discount percentage)

Using the formula X * P% = Y, we can calculate the amount of discount as

Y = X * P% = 100 * 0.20 = 20

So, the customer will pay 100 - 20 = \$80 after the discount.

Q2. A student scored 85% marks in a test. If the test had 20 questions, how many questions did the student answer correctly?

Solution:

Let X = 20 (number of questions in the test) and P% = 0.85 (percentage of marks scored by the student)

Using the formula X * P% = Y, we can calculate the number of questions answered correctly as Y = X * P% = 20 * 0.85 = 17

So, the student answered 17 questions correctly.

Q3. A company's profits increased by 50% from the previous year. If the profits were \$500,000 last year, how much did the company make this year?

Solution:

Let X = 500,000 (profits last year) and P% = 0.50 (percentage increase in profits)

Using the formula X * P% = Y, we can calculate the increase in profits as Y = X * P% = 500,000 * 0.50 = 250,000

Therefore, the company's profits this year are 500,000 + 250,000 = \$750,000

Q4. A recipe calls for 2 cups of sugar for every 5 cups of flour. How much sugar is needed for 8 cups of flour?

Solution:

Let X=5 (cups of flour) and P% = 2/5 (cups of sugar per cups of flour)

Using the formula X * P% = Y, we can calculate the amount of sugar needed as Y = X * P% = 8 * (2/5) = 3.2 cups

So, 3.2 cups of sugar is needed for 8 cups of flour.

### Type 2 - Y/X = P%

The formula Y/X = P% can be used to calculate the percentage of a number X.

Y is the part of the whole and P% is the percentage expressed as a decimal.

Example 1:

If X = 100 and Y = 25, then

P% = Y/X = 25/100 = 0.25

This means that 25 is 25% of 100 when you convert decimal 0.25 to percent by dividing it by 100

0.25/100 =  25%

Example 2:

If X = 500 and Y = 50, then

P% = Y/X = 50/500 = 0.1

This means that 50 is 10% of 500.

Example 3:

If X = 1000 and Y = 50, then

P% = Y/X = 50/1000 = 0.05

This means that 50 is 5% of 1000.

You can also express P% in percentage form by multiplying with 100, P% = Y/X * 100

### Examples of Questions using  Y/X = P%

Q1. A student scored 75 out of 100 in a test. What percentage did the student score?

Solution:

Let X = 100 (total marks in the test) and Y = 75 (marks scored by the student)

Using the formula Y/X = P%, we can calculate the percentage as P% = Y/X = 75/100 = 0.75

Therefore, the student scored 75% in the test.

Q2. A car traveled 150 miles on 5 gallons of gasoline. What is the mileage of the car?

Solution:

Let X = 5 (gallons of gasoline) and Y = 150 (miles traveled)

Using the formula Y/X = P%, we can calculate the mileage as P% = Y/X = 150/5 = 30

Therefore, the car has a mileage of 30 miles per gallon.

Q3. A box contains 24 chocolates out of which 12 are dark chocolates. What percentage of chocolates are dark chocolates?

Solution:

Let X = 24 (total number of chocolates) and Y = 12 (number of dark chocolates)

Using the formula Y/X = P%, we can calculate the percentage as P% = Y/X = 12/24 = 0.5

Therefore, 50% of the chocolates in the box are dark chocolates.

Q4. A company's profits increased by \$500,000 from the previous year. If the profits were \$1,000,000 last year, what percentage increase in profits was there?

Solution:

Let X = 1000000 (profits last year) and Y = 500000 (increase in profits)

Using the formula Y/X = P%, we can calculate the percentage as P% = Y/X = 500000/1000000 = 0.5

Therefore, the company's profits increased by 50%.

### Type 3 - Y/P% = X

The formula Y/P% = X can be used to calculate the whole number X based on the percentage P% and the part of the whole Y. P% is the percentage expressed as a decimal (e.g. 25% is 0.25).

Example 1:

If Y = 25 and P% = 0.25, then X = Y/P% = 25/0.25 = 100

This means that 25 is 25% of 100.

Example 2:

If Y = 50 and P% = 0.1, then X = Y/P% = 50/0.1 = 500

This means that 50 is 10% of 500.

Example 3:

If Y = 50 and P% = 0.05, then X = Y/P% = 50/0.05 = 1000

This means that 50 is 5% of 1000.

It is important to notice that this formula is similar to Y/X = P% where X is being calculated. This formula is useful when you know the part of the whole and the percentage but not the whole.

Also please note that if you want to express P% in percentage form, you need to multiply with 100.

### Examples of Questions using  Y/X = P%

Q1. A student scored 75 out of 100 in a test. What is the total marks of the test?

Solution:

Let Y = 75 (marks scored by the student) and P% = 0.75 (percentage scored by the student)

Using the formula Y/P% = X, we can calculate the total marks as X = Y/P% = 75/0.75 = 100

Therefore, the total marks in the test are 100.

Q2. A car traveled 150 miles on 5 gallons of gasoline. What is the total distance the car can travel with 20 gallons of gasoline?

Solution:

Let Y = 150 (miles traveled on 5 gallons) and P% = 5/150 = 1/30 (mileage of the car)

Using the formula Y/P% = X, we can calculate the total distance as X = Y/P% = 20 * (1/30) = 20/30 = 20/3 = 666.67 miles

Therefore, the car can travel 666.67 miles on 20 gallons of gasoline.

Q3. A box contains 24 chocolates out of which 12 are dark chocolates. How many chocolates are there in the box if 25% of them are dark chocolates?

Solution:

Let Y = 12 (number of dark chocolates) and P% = 0.25 (percentage of dark chocolates)

Using the formula Y/P% = X, we can calculate the total number of chocolates as X = Y/P% = 12/0.25 = 48

Therefore, there are 48 chocolates in the box.

Q4. A company's profits increased by \$500,000 from the previous year. If the profits increased by 20%, what were the profits last year?

Solution:

Let Y = 500000 (increase in profits) and P% = 0.2 (percentage increase in profits)

Using the formula Y/P% = X, we can calculate the profits last year as X = Y/P% = 500000/0.2 = 2,500,000

Therefore, the company's profits last year were \$2,500,000.

Please note that in the last example, you can express P% in percentage form by multiplying with 100, P% = Y/X * 100 = 0.2 * 100 = 20%.

### Type 5 - X * (1 + P%) = Y

The formula X * (1 + P%) = Y can be used to calculate the final value Y after an increase or decrease of a certain percentage P% on a starting value X. P% is the percentage expressed as a decimal (e.g. 25% is 0.25). The term (1 + P%) is known as the growth factor.

Example 1:

If X = 100 and P% = 0.25, then Y = X * (1 + P%) = 100 * (1 + 0.25) = 100 * 1.25 = 125

This means that an increase of 25% on 100 results in 125.

Example 2:

If X = 500 and P% = -0.1, then Y = X * (1 + P%) = 500 * (1 - 0.1) = 500 * 0.9 = 450

This means that a decrease of 10% on 500 results in 450.

Example 3:

If X = 1000 and P% = 0.05, then Y = X * (1 + P%) = 1000 * (1 + 0.05) = 1000 * 1.05 = 1050

This means that an increase of 5% on 1000 results in 1050.

This formula is useful when you want to calculate the final value after a percentage increase or decrease. It is also known as the percentage change formula.

Q1. A store is offering a 20% increase on the price of a product. If the original price of the product is \$100, what is the new price after the increase?

Solution:

Let X = 100 (original price) and P% = 0.20 (percentage increase)

Using the formula X * (1 + P%) = Y, we can calculate the new price as Y = X * (1 + P%) = 100 * (1 + 0.20) = 100 * 1.20 = \$120

Therefore, the new price of the product is \$120.

Q2. An investor invested \$1000 in a stock that decreased by 10%. How much did the investment decrease in value?

Solution:

Let X = 1000 (original investment) and P% = -0.10 (percentage decrease)

Using the formula X * (1 + P%) = Y, we can calculate the decrease in value as Y = X * (1 + P%) = 1000 * (1 - 0.10) = 1000 * 0.90 = \$900

Therefore, the investment decreased in value by \$100.

Q3. A company is offering a 5% raise to its employees. If an employee's salary is \$50,000, what will be the employee's new salary after the raise?

Solution:

Let X = 50000 (original salary) and P% = 0.05 (percentage raise)

Using the formula X * (1 + P%) = Y, we can calculate the new salary as Y = X * (1 + P%) = 50000 * (1 + 0.05) = 50000 * 1.05 = \$52,500

Therefore, the employee's new salary after the raise is \$52,500.

Q4. A stock decreased by 15%. If it was worth \$5000, what is its worth now?

Solution:

Let X = 5000 (original stock value) and P% = -0.15 (percentage decrease)

Using the formula X * (1 + P%) = Y, we can calculate the new value as Y = X * (1 + P%) = 5000 * (1 - 0.15) = 5000 * 0.85 = \$4250

Therefore, the stock worth now is \$4250

Please note that in the last example, P% is negative because the stock decreased in value.

It's important to understand that the value P% can be positive or negative depending on the scenario, representing an increase or decrease respectively.

### Type 6 -Y/1+P% = X

The formula Y/1+P% = X can be used to calculate the original value X before a percentage increase or decrease, based on the final value Y and the percentage change P%. P% is the percentage change expressed as a decimal (e.g. 25% increase is 0.25, 10% decrease is -0.1) and (1+P%) is known as the percentage change factor.

Example 1:

If Y = 125 and P% = 0.25, then X = Y/(1+P%) = 125/(1+0.25) = 125/1.25 = 100

This means that an increase of 25% on 100 results in 125.

Example 2:

If Y = 450 and P% = -0.1, then X = Y/(1+P%) = 450/(1-0.1) = 450/0.9 = 500

This means that a decrease of 10% on 500 results in 450.

Example 3:

If Y = 1050 and P% = 0.05, then X = Y/(1+P%) = 1050/(1+0.05) = 1050/1.05 = 1000

This means that an increase of 5% on 1000 results in 1050.

This formula is useful when you want to calculate the original value before a percentage increase or decrease, It is also known as the inverse percentage change formula.

### Examples of Questions using - Y/1+P% = X

Q1. The price of a product was increased by 25%. If the new price is \$125, what was the original price?

Solution:

Let Y = 125 (new price) and P% = 0.25 (percentage increase)

Using the formula Y/1+P% = X, we can calculate the original price as X = Y/(1+P%) = 125/(1+0.25) = 125/1.25 = \$100

Therefore, the original price of the product was \$100.

Q2. An investment decreased by 10%. If its current value is \$900, what was its original value?

Solution:

Let Y = 900 (current value) and P% = -0.10 (percentage decrease)

Using the formula Y/1+P% = X, we can calculate the original value as X = Y/(1+P%) = 900/(1-0.10) = 900/0.9 = \$1000

Therefore, the original value of the investment was \$1000.

Q3. An employee's salary was increased by 5%. If the new salary is \$52,500, what was the original salary?

Solution:

Let Y = 52500 (new salary) and P% = 0.05 (percentage increase)

Using the formula Y/1+P% = X, we can calculate the original

## Types of Percent Calculators

### Percentage Change Calculator

When you wish to calculate the percentage change from one number to the other, the Percent Change Calculator comes into action. This change is usually expressed as percentage increase or percentage decrease. For instance, first you had 10 cookies and now you have 20. Then you had a 100% increase in your cookies count.

This percentage change calculator only works if there is an initial and final value. Without any one, it is of no use. When the change is positive, it denotes the increase in percentage value and if the change is negative, it denotes the decrease in the value.

If the numbers’ order matters to you, then the percentage change calculator is used with the initial and final value.

The Percentage change is derived by dividing the change in value by the absolute value of the initial value and then multiplying it by 100. Let’s explain this in detail with an example.

Using the formula: (New value - Old value) / Old value * 100 = percent change

If the price of a product was \$100 and it increased to \$125, you can use the formula: (125 - 100) / 100 * 100 = 25%. This means that the price of the product increased by 25%.

For example, if a company's profits were \$1 million last year and \$1.2 million this year, you can use the formula: (1.2 - 1) / 1 * 100 = 20%. This means that the company's profits have increased by 20% this year.

if you have the current value and the original value and you want to find the percent change, you can use the formula: (New value - Old value) / Old value * 100

For example, if an employee's salary was \$50,000 and now it's \$52,500. you can use the formula: (52,500-50,000)/50,000 * 100 = 5%.

This means that the employee's salary increased by 5%

More Examples

Q1. If a product's original price was \$100 and it's now \$120, the percentage difference can be calculated as:

Solution - (|120 - 100| / (120 + 100) * 2) * 100 = (20 / 220) * 100 = 9.09%.

This means that the product's price has increased by 9.09%

Q2 - If a company's profit was \$1,000,000 and it's now \$900,000, the percentage difference can be calculated as:

Solution -(|900,000 - 1,000,000| / (900,000 + 1,000,000) * 2) * 100 = (100,000 / 2,000,000) * 100 = 5%.

This means that the company's profit has decreased by 5%.

Q3. If a stock was trading at \$50 and it's now trading at \$60, the percentage difference can be calculated as:

Solution - (|60-50| / (60+50) * 2) * 100 = (10 / 110) * 100 = 9.09%. This means that the stock has increased by 9.09%

The formula calculates the absolute difference between the two values. Therefore, the result is always positive.

### Fraction to Percent Calculator

With the Fraction to Percent Calculator, you can convert any proper and improper fractions to percentage.

Formula - Fraction * 100 = Percentage

This can be done in two easy steps:

1. Convert the fraction to a decimal value.
To do this you just need to divide the numerator from the denominator. For instance, in 3/4 , 3 is the numerator and 4 is the denominator. You divide 3 from 4 and get 0.75 as the decimal value.

3/4 = 3 ÷ 4 = 0.75

2. Multiply the decimal value by 100 to get the percentage value.

This goes as it says. Multiply the decimal value, i.e. 0.75 by 100 to get the percent value, 75%.

0.75 x 100 = 75%

You can also reduce the fraction to the minimum value, before converting it to a decimal, to make the division easier. The final answer will be the same.

Examples

1. If you have 1/4 of a pizza and you want to know what percentage of the pizza it is, you can use the formula: 1/4 * 100 = 25%. This means that 1/4 of the pizza is 25%.
2. If you have 3/8 of a cake and you want to know what percentage of the cake it is, you can use the formula: 3/8 * 100 = 37.5%. This means that 3/8 of the cake is 37.5%.
3. If you have 2/5 of a book read, and you want to know what percentage of the book you have read, you can use the formula: 2/5 * 100 = 40%. This means that you have read 40% of the book.

You can also convert a decimal to a percentage by multiplying it by 100 and adding the percentage sign(%). For example, 0.5 as a decimal is 50% as a percentage.

It's important to notice that if you are converting a fraction to a percentage, the fraction must be simplified first, otherwise, you will get an incorrect result.

### Percent to Fraction Calculator

The Percent to Fraction Calculator also helps in converting a percent to a fraction. When the percent value is more than 100%, it is first converted to a mixed fraction.

Formula  - Percentage / 100 = Fraction

To convert the percent value to fraction, it is first converted into a decimal value and then into a fraction. The percent value can also be in decimal, for eg; 6.25% or 0.56%.

Converting a Percent to Fraction

1. First step would be to divide the percentage value by 100 to obtain a decimal value.
2. The number on the top will be treated as the numerator and place 1 as the denominator of the fraction.
3. Converting decimal to a whole number. Count the number of places there are on the right of the decimal. For instance, you have 2 decimal places, then multiply the numerator and denominator by 20 (10*2).
4. Reducing the fraction. To reduce the fraction, find the GCF (Greatest Common Factor) of both numerator and denominator. Then, divide the numerator and denominator by GCF and reduce the fraction.
5. If possible, you can also simplify the remaining fraction value to a mixed fraction.

Examples -

1. If you have 25% of a pizza and you want to know what fraction of the pizza it is, you can use the formula: 25 / 100 = 1/4. This means that 25% of the pizza is 1/4.
2. If you have 37.5% of a cake and you want to know what fraction of the cake it is, you can use the formula: 37.5 / 100 = 3/8. This means that 37.5% of the cake is 3/8.
3. If you have 40% of a book read, and you want to know what fraction of the book you have read, you can use the formula: 40 / 100 = 2/5. This means that you have read 2/5 of the book.

You can also convert a decimal to a fraction by dividing the decimal by 1 and expressing the result in the form of a fraction. For example, 0.5 as a decimal is 1/2 as a fraction.

It's important to note that when you convert a percentage to a fraction, the resulting fraction will be in its simplest form.

### Percent to Decimal Calculator

The Percent to Decimal calculator divides the percent value by 100 to convert it to the decimal value. You just input the percent value and it shows the result, which is a decimal value.

Formula - Percentage / 100 = Decimal

### Converting a Percent to a Decimal

To convert a percent value to a decimal, you just divide the percent by 100 and remove the percentage sign. For instance, to convert 20% to a decimal, 20% becomes 20/100 = 0.20. An easier way to convert a percent to a decimal is that the percent sign be removed and the decimal point is moved 2 places to the left.

Examples -

If you have 25% and you want to know what decimal it is, you can use the formula: 25 / 100 = 0.25. This means that 25% is 0.25 as a decimal.

1. If you have 37.5% and you want to know what decimal it is, you can use the formula: 37.5 / 100 = 0.375. This means that 37.5% is 0.375 as a decimal.
2. If you have 40% and you want to know what decimal it is, you can use the formula: 40 / 100 = 0.4. This means that 40% is 0.4 as a decimal.

It's important to note that when you convert a percentage to a decimal, you always divide the percentage by 100.

It's also important to note that a decimal is a way of expressing a number in base 10, while a percentage is a way of expressing a proportion as a fraction of 100.

### Decimal to Percent Calculator

With the Decimal to Percent calculator, you can easily convert the whole number and even the decimal part of a number to a percent value.

Formula - Decimal x 100 = Percentage

To convert a decimal to percent, you just multiply the number by 100 and add the percent sign at the end. For instance, to convert 0.20 into percent, 0.20 becomes 0.20 x 100 = 20%. Similarly, 0.275 becomes 0.275 x 100 = 27.5%.

Another easier way to convert decimal to percent is to move the decimal point 2 places to the right and then add %.

Examples

1. If you have 0.25 as a decimal and you want to know what percentage it is, you can use the formula: 0.25 x 100 = 25%. This means that 0.25 as a decimal is 25% as a percentage.
2. If you have 0.375 as a decimal and you want to know what percentage it is, you can use the formula: 0.375 x 100 = 37.5%. This means that 0.375 as a decimal is 37.5% as a percentage.
3. If you have 0.4 as a decimal and you want to know what percentage it is, you can use the formula: 0.4 x 100 = 40%. This means that 0.4 as a decimal is 40% as a percentage.

It's important to note that when you convert a decimal to a percentage, you always multiply the decimal by 100.

It's also important to note that a decimal is a way of expressing a number in base 10, while a percentage is a way of expressing a proportion as a fraction of 100.