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How to Solve Percent Problems? (+FREE Worksheet!)

Learn how to calculate and solve percent problems using the percent formula.

Related Topics

• How to Find Percent of Increase and Decrease
• How to Find Discount, Tax, and Tip
• How to Do Percentage Calculations
• How to Solve Simple Interest Problems

Step by step guide to solve percent problems

• In each percent problem, we are looking for the base, or part or the percent.
• Use the following equations to find each missing section. Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(\color{ black }{Part} = \color{blue}{Percent} \ ×\) Base \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base

Percent Problems – Example 1:

\(2.5\) is what percent of \(20\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=2.5 \ ÷ \ 20=0.125=12.5\%\)

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Percent problems – example 2:.

\(40\) is \(10\%\) of what number?

Use the following formula: Base \(= \color{ black }{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=40 \ ÷ \ 0.10=400\) \(40\) is \(10\%\) of \(400\).

Percent Problems – Example 3:

\(1.2\) is what percent of \(24\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=1.2÷24=0.05=5\%\)

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Percent problems – example 4:.

\(20\) is \(5\%\) of what number?

Use the following formula: Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=20÷0.05=400\) \( 20\) is \(5\%\) of \(400\).

Exercises for Calculating Percent Problems

Solve each problem..

• \(51\) is \(340\%\) of what?
• \(93\%\) of what number is \(97\)?
• \(27\%\) of \(142\) is what number?
• What percent of \(125\) is \(29.3\)?
• \(60\) is what percent of \(126\)?
• \(67\) is \(67\%\) of what?

Download Percent Problems Worksheet

• \(\color{blue}{15}\)
• \(\color{blue}{104.3}\)
• \(\color{blue}{38.34}\)
• \(\color{blue}{23.44\%}\)
• \(\color{blue}{47.6\%}\)
• \(\color{blue}{100}\)

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by: Effortless Math Team about 4 years ago (category: Articles , Free Math Worksheets )

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Percentage Word Problems

Welcome to our Basic Percentage Word Problems. In this area, we have a selection of basic percentage problem worksheets designed for 6th grade students who are just starting to learn about percentages to help them to solve a range of simple percentage problems.

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Percentage Learning

Percentages are another area that children can find quite difficult. There are several key areas within percentages which need to be mastered in order.

Our selection of percentage worksheets will help you to find percentages of numbers and amounts, as well as working out percentage increases and decreases and converting percentages to fractions or decimals.

Key percentage facts:

• 50% = 0.5 = ½
• 25% = 0.25 = ¼
• 75% = 0.75 = ¾
• 10% = 0.1 = 1 ⁄ 10
• 1% = 0.01 = 1 ⁄ 100

How to work out Percentages of a number

This page will help you learn to find the percentage of a given number.

There is also a percentage calculator on the page to support you work through practice questions.

• Percentage Of Calculator

This is the calculator to use if you want to find a percentage of a number.

Simple choose your number and the percentage and the calculator will do the rest.

Basic Percentage Word Problems

Here you will find a selection of worksheets on percentages designed to help your child practise how to apply their knowledge to solve a range of percentage problems..

The sheets are graded so that the easier ones are at the top.

The sheets have been split up into sections as follows:

• spot the percentage problems where the aim is to use the given facts to find the missing percentage;
• solving percentage of number problems, where the aim is to work out the percentage of a number.

Each of the sheets on this page has also been split into 3 different worksheets:

• Sheet A which is set at an easier level;
• Sheet B which is set at a medium level;
• Sheet C which is set at a more advanced level for high attainers.

Spot the Percentages Problems

• Spot the Percentage 1A
• PDF version
• Spot the Percentage 1B
• Spot the Percentage 1C
• Spot the Percentage 2A
• Spot the Percentage 2B
• Spot the Percentage 2C

Percentage of Number Word Problems

• Percentage of Number Problems 1A
• Percentage of Number Problems 1B
• Percentage of Number Problems 1C
• Percentage of Number Problems 2A
• Percentage of Number Problems 2B
• Percentage of Number Problems 2C
• Percentage of Number Problems 3A
• Percentage of Number Problems 3B
• Percentage of Number Problems 3C

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

6th Grade Percentage Word Problems

The sheets in this area are at a harder level than those on this page.

The problems involve finding the percentage of numbers and amounts, as well as finding the amounts when the percentage is given.

• 6th Grade Percent Word Problems
• Percentage Increase and Decrease Worksheets

We have created a range of worksheets based around percentage increases and decreases.

Our worksheets include:

• finding percentage change between two numbers;
• finding a given percentage increase from an amount;
• finding a given percentage decrease from an amount.

Percentage of Money Amounts

Often when we are studying percentages, we look at them in the context of money.

The sheets on this page are all about finding percentages of different amounts of money.

• Money Percentage Worksheets

Percentage of Number Worksheets

If you would like some practice finding the percentage of a range of numbers, then try our Percentage Worksheets page.

You will find a range of worksheets starting with finding simple percentages such as 1%, 10% and 50% to finding much trickier ones.

• Percentage of Numbers Worksheets

Converting Percentages to Fractions

To convert a fraction to a percentage follows on simply from converting a fraction to a decimal.

Simply divide the numerator by the denominator to give you the decimal form. Then multiply the result by 100 to change the decimal into a percentage.

The printable learning fraction page below contains more support, examples and practice converting fractions to decimals.

• Converting Fractions to Percentages

• Convert Percent to Fraction

Online Percentage Practice Zone

Our online percentage practice zone gives you a chance to practice finding percentages of a range of numbers.

You can choose your level of difficulty and test yourself with immediate feedback!

• Online Percentage Practice
• Ratio Part to Part Worksheets

These sheets are a great way to introduce ratio of one object to another using visual aids.

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Percentage Questions

Percentage Questions with answers are provided here. Students can practise these questions based on percentages to prepare for the upcoming exams. These percentage problems are prepared by our subject experts, as per the latest exam pattern. All the materials here are formulated according to the NCERT curriculum and the latest CBSE syllabus (2022-2023). Learn How to Calculate Percentage here at BYJU’S with easy steps.

Definition: Percentage is derived from the Latin word “per centum”. It means by the hundred. It is denoted by %. If we say, 5%, then it is equal to 5/100 = 0.05.

Percentage Questions and Solutions

Q.1: A fruit seller had some apples. He sells 40% apples and still has 420 apples. What is the total number of apples he had originally?

Solution: Let the number of apples a fruit seller had be x.

As per the given question,

(100 – 40%) of x = 420

60% of x = 420

60/100 x = 420

Hence, the fruit seller had a total of 700 apples

Q.2: A person multiplied a number by 3/5 instead of 5/3, What is the percentage error in the calculation?

Solution: Let the number be X.

X is mistakenly multiplied by ⅗ = 3X/5

X should be multiplied by 5/3 = 5X/3

Thus, the error will be = (5X/3 – 3x/5) = 16X/15

Percentage Error = (error/True value) x 100

= [(16/15) x X/(5/3) x X] x 100

Q.3: If 20% of x = y, what is the value of y% of 20 in terms of x?

Solution: Given,

20% of x = y

⇒ (20/100) x = y

=(y/100). 20

= [(20x/100) / 100] x 20

Q.4: Three students contested an election and received 1000, 5000 and 10000 votes, respectively. What is the percentage of the total votes the winning student gets?

Solution: Total number of votes = 1000 + 5000 + 10000 = 16000

The student who won the votes got 10000 votes

Hence, the percentage will be:

(10000/16000) x 100% = 62.5%

Q.5: If the price of a product is first decreased by 25% and then increased by 20%, then what is the percentage change in the price?

Solution: Let the original price be Rs. 100.

New final price = 120 % of (75 % of Rs. 100)

Therefore, the net change in price is 100 – 90 = 10.

Percentage decrease = 10%

Q.6: The value of a washing machine depreciates at the rate of 10% every year. If its present value is Rs. 8748, then what was the price of the washing machine three years ago?

Current price of the washing machine = Rs.8748

The price of the machine depreciated at the rate of 10% every year

Therefore, the price of the washing machine three years ago = 8748 ÷ (1 – 10/100) 3

Q.7: For a student to clear an examination, he must score 55% marks. If he gets 120 and fails by 78 marks, what is the total marks for the examination?

Solution: Given, the mark obtained by the student is 120 and the student fails by 78 marks

Therefore, the passing marks is = 120+78 = 198

Let us consider, the total marks be x

⇒ (55/100) × x = 198

Q.8: By how much is 80% of 40 greater than 4/5 of 25?

Solution: 80% of 40 = 80/100 × 40

⅘ of 25 = ⅘ × 25

Required value = (80/100) × 40 – (4/5) × 25

= 32 – 20

Q.9: A number is decreased by 10% and then increased by 10%. The number so obtained is 10 less than the original number. What was the original number?

Solution: Let the original number be x

Final number obtained = 110% of (90% of x)

=(110/100 × 90/100 × x)

= (99/100)x

Given the number obtained is 10 less than the original number.

x – (99/100) x = 10

Q.10: What is the percentage of ratio 5:4?

Solution: 5 : 4 = 5/4 = ( (5/4) x 100 )% = 125%.

Related Articles

• Percent Error
• Percentage Increase Or Decrease
• Loss Percentage Formula
• Fraction to Percent Conversion
• Difference Between Percentage and Percentile

Practice Questions on Percentage

• What is 25% of 80?
• What is the percentage of 50 paise to 4 rupees?
• Find the percentage change, when a number is changed from 100 to 80.
• 50 is what percentage of 500?

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4.2: Percents Problems and Applications of Percent

• Last updated
• Save as PDF
• Page ID 142718

• Morgan Chase
• Clackamas Community College via OpenOregon

You may use a calculator throughout this module.

Recall: The amount is the answer we get after finding the percent of the original number. The base is the original number, the number we find the percent of. We can call the percent the rate.

When we looked at percents in a previous module, we focused on finding the amount. In this module, we will learn how to find the percentage rate and the base.

\(\text{Amount}=\text{Rate}\cdot\text{Base}\)

\(A=R\cdot{B}\)

We can translate from words into algebra.

• “is” means equals
• “of” means multiply
• “what” means a variable

Solving Percent Problems: Finding the Rate

Suppose you earned \(56\) points on a \(60\)-point quiz. To figure out your grade as a percent, you need to answer the question “\(56\) is what percent of \(60\)?” We can translate this sentence into the equation \(56=R\cdot60\).

Exercises \(\PageIndex{1}\)

1. \(56\) is what percent of \(60\)?

2. What percent of \(120\) is \(45\)?

1. \(93\%\) or \(93.3\%\)

2. \(37.5\%\)

Be aware that this method gives us the answer in decimal form and we must move the decimal point to convert the answer to a percent.

Also, if the instructions don’t explicitly tell you how to round your answer, use your best judgment: to the nearest whole percent or nearest tenth of a percent, to two or three significant figures, etc.

Solving Percent Problems: Finding the Base

Suppose you earn \(2\%\) cash rewards for the amount you charge on your credit card. If you want to earn $ \(50\) in cash rewards, how much do you need to charge on your card? To figure this out, you need to answer the question “\(50\) is \(2\%\) of what number?” We can translate this into the equation \(50=0.02\cdot{B}\).

3. $ \(50\) is \(2\%\) of what number?

4. \(5\%\) of what number is \(36\)?

3. $ \(2,500\)

5. An \(18\%\) tip will be added to a dinner that cost $ \(107.50\). What is the amount of the tip?

6. The University of Oregon women’s basketball team made \(13\) of the \(29\) three-points shots they attempted during a game against UNC. What percent of their three-point shots did the team make?

7. \(45\%\) of the people surveyed answered “yes” to a poll question. If \(180\) people answered “yes”, how many people were surveyed altogether?

5. $ \(19.35\)

6. \(44.8\%\) or \(45\%\)

7. \(400\) people were surveyed

Solving Percent Problems: Percent Increase

When a quantity changes, it is often useful to know by what percent it changed. If the price of a candy bar is increased by \(50\) cents, you might be annoyed because it’s it’s a relatively large percentage of the original price. If the price of a car is increased by \(50\) cents, though, you wouldn’t care because it’s such a small percentage of the original price.

To find the percent of increase:

• Subtract the two numbers to find the amount of increase.
• Using this result as the amount and the original number as the base, find the unknown percent.

Notice that we always use the original number for the base, the number that occurred earlier in time. In the case of a percent increase, this is the smaller of the two numbers.

8. The price of a candy bar increased from $ \(0.89\) to $ \(1.39\). By what percent did the price increase?

9. The population of Portland in 2010 was \(583,793\). The estimated population in 2019 was \(654,741\). Find the percent of increase in the population. [1]

8. \(56.2\%\) increase

9. \(12.2\%\) increase

Solving Percent Problems: Percent Decrease

Finding the percent decrease in a number is very similar.

To find the percent of decrease:

• Subtract the two numbers to find the amount of decrease.

Again, we always use the original number for the base, the number that occurred earlier in time. For a percent decrease, this is the larger of the two numbers.

10. During a sale, the price of a candy bar was reduced from $ \(1.39\) to $ \(0.89\). By what percent did the price decrease?

11. The number of students enrolled at Clackamas Community College decreased from \(7,439\) in Summer 2019 to \(4,781\) in Summer 2020. Find the percent of decrease in enrollment.

10. \(36.0\%\) decrease

11. \(35.7\%\) decrease

Relative Error

In an earlier module, we said that a measurement will always include some error, no matter how carefully we measure. It can be helpful to consider the size of the error relative to the size of what is being measured. As we saw in the examples above, a difference of \(50\) cents is important when we’re pricing candy bars but insignificant when we’re pricing cars. In the same way, an error of an eighth of an inch could be a deal-breaker when you’re trying to fit a screen into a window frame, but an eighth of an inch is insignificant when you’re measuring the length of your garage.

The expected outcome is what the number would be in a perfect world. If a window screen is supposed to be exactly \(25\) inches wide, we call this the expected outcome, and we treat it as though it has infinitely many significant digits. In theory, the expected outcome is \(25.000000...\)

To find the absolute error , we subtract the measurement and the expected outcome. Because we always treat the expected outcome as though it has unlimited significant figures, the absolute error should have the same precision (place value) as the measurement , not the expected outcome .

To find the relative error , we divide the absolute error by the expected outcome. We usually express the relative error as a percent. In fact, the procedure for finding the relative error is identical to the procedures for finding a percent increase or percent decrease!

To find the relative error:

• Subtract the two numbers to find the absolute error.
• Using the absolute error as the amount and the expected outcome as the base, find the unknown percent.

Exercisew \(\PageIndex{1}\)

12. A window screen is measured to be \(25\dfrac{3}{16}\) inches wide instead of the advertised \(25\) inches. Determine the relative error, rounded to the nearest tenth of a percent.

13. The contents of a box of cereal are supposed to weigh \(10.8\) ounces, but they are measured at \(10.67\) ounces. Determine the relative error, rounded to the nearest tenth of a percent.

12. \(0.1875\div25\approx0.8\%\)

13. \(0.13\div10.8\approx1.2\%\)

The tolerance is the maximum amount that a measurement is allowed to differ from the expected outcome. For example, the U.S. Mint needs its coins to have a consistent size and weight so that they will work in vending machines. A dime (10 cents) weighs \(2.268\) grams, with a tolerance of \(\pm0.091\) grams. [2] This tells us that the minimum acceptable weight is \(2.268-0.091=2.177\) grams, and the maximum acceptable weight is \(2.268+0.091=2.359\) grams. A dime with a weight outside of the range \(2.177\leq\text{weight}\leq2.359\) would be unacceptable.

A U.S. nickel (5 cents) weighs \(5.000\) grams with a tolerance of \(\pm0.194\) grams.

14. Determine the lowest acceptable weight and highest acceptable weight of a nickel.

15. Determine the relative error of a nickel that weighs \(5.21\) grams.

A U.S. quarter (25 cents) weighs \(5.670\) grams with a tolerance of \(\pm0.227\) grams.

16. Determine the lowest acceptable weight and highest acceptable weight of a quarter.

17. Determine the relative error of a quarter that weighs \(5.43\) grams.

14. \(4.806\) g; \(5.194\) g

15. \(0.21\div5.000=4.2\%\)

16. \(5.443\) g; \(5.897\) g

17. \(0.24\div5.670\approx4.2\%\)

• www.census.gov/quickfacts/fact/table/portlandcityoregon,OR,US/PST045219 ↵
• https://www.usmint.gov/learn/coin-and-medal-programs/coin-specifications and https://www.thesprucecrafts.com/how-much-do-coins-weigh-4171330 ↵

Solving Percent Problems

Learning Objective(s)

·          Identify the amount, the base, and the percent in a percent problem.

·          Find the unknown in a percent problem.

Introduction

Percents are a ratio of a number and 100. So they are easier to compare than fractions, as they always have the same denominator, 100. A store may have a 10% off sale. The amount saved is always the same portion or fraction of the price, but a higher price means more money is taken off. Interest rates on a saving account work in the same way. The more money you put in your account, the more money you get in interest. It’s helpful to understand how these percents are calculated.

Parts of a Percent Problem

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off the original $220 price.

Problems involving percents have any three quantities to work with: the percent , the amount , and the base .

The percent has the percent symbol (%) or the word “percent.” In the problem above, 15% is the percent off the purchase price.

The base is the whole amount. In the problem above, the whole price of the guitar is $220, which is the base.

The amount is the number that relates to the percent. It is always part of the whole. In the problem above, the amount is unknown. Since the percent is the percent off , the amount will be the amount off of the price .

You will return to this problem a bit later. The following examples show how to identify the three parts, the percent, the base, and the amount.

The previous problem states that 30 is a portion of another number. That means 30 is the amount. Note that this problem could be rewritten: 20% of what number is 30?

Solving with Equations

Percent problems can be solved by writing equations. An equation uses an equal sign (= ) to show that two mathematical expressions have the same value.

Percents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of another amount, you multiply.

The percent of the base is the amount.

Percent of the Base is the Amount.

Percent · Base = Amount

Once you have an equation, you can solve it and find the unknown value. To do this, think about the relationship between multiplication and division. Look at the pairs of multiplication and division facts below, and look for a pattern in each row.

Multiplication and division are inverse operations. What one does to a number, the other “undoes.”

When you have an equation such as 20% · n = 30, you can divide 30 by 20% to find the unknown: n =  30 ÷ 20%.

You can solve this by writing the percent as a decimal or fraction and then dividing.

n = 30 ÷ 20% =  30 ÷ 0.20 = 150

You can estimate to see if the answer is reasonable. Use 10% and 20%, numbers close to 12.5%, to see if they get you close to the answer.

10% of 72 = 0.1 · 72 = 7.2

20% of 72 = 0.2 · 72 = 14.4

Notice that 9 is between 7.2 and 14.4, so 12.5% is reasonable since it is between 10% and 20%.

This problem is a little easier to estimate. 100% of 24 is 24. And 110% is a little bit more than 24. So, 26.4 is a reasonable answer.

Using Proportions to Solve Percent Problems

Let’s go back to the problem that was posed at the beginning. You can now solve this problem as shown in the following example.

You can estimate to see if the answer is reasonable. Since 15% is half way between 10% and 20%, find these numbers.

10% of 220 = 0.1 · 220 = 22

20% of 220 = 0.2 · 220 = 44

The answer, 33, is between 22 and 44. So $33 seems reasonable.

There are many other situations that involve percents. Below are just a few.

Percentages Worksheets

Welcome to the percentages math worksheet page where we are 100% committed to providing excellent math worksheets. This page includes Percentages worksheets including calculating percentages of a number, percentage rates, and original amounts and percentage increase and decrease worksheets.

As you probably know, percentages are a special kind of decimal. Most calculations involving percentages involve using the percentage in its decimal form. This is achieved by dividing the percentage amount by 100. There are many worksheets on percentages below. In the first few sections, there are worksheets involving the three main types of percentage problems: calculating the percentage value of a number, calculating the percentage rate of one number compared to another number, and calculating the original amount given the percentage value and the percentage rate.

Most Popular Percentages Worksheets this Week

Percentage Calculations

Calculating the percentage value of a number involves a little bit of multiplication. One should be familiar with decimal multiplication and decimal place value before working with percentage values. The percentage value needs to be converted to a decimal by dividing by 100. 18%, for example is 18 ÷ 100 = 0.18. When a question asks for a percentage value of a number, it is asking you to multiply the two numbers together.

Example question: What is 18% of 2800? Answer: Convert 18% to a decimal and multiply by 2800. 2800 × 0.18 = 504. 504 is 18% of 2800.

• Calculating the Percentage Value (Whole Number Results) Calculating the Percentage Value (Whole Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Number Results) (Select percents) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 25%)
• Calculating the Percentage Value (Decimal Number Results) Calculating the Percentage Value (Decimal Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Number Results) (Select percents) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 25%)
• Calculating the Percentage Value (Whole Dollar Results) Calculating the Percentage Value (Whole Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Dollar Results) (Select percents) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 25%)
• Calculating the Percentage Value (Decimal Dollar Results) Calculating the Percentage Value (Decimal Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Dollar Results) (Select percents) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 25%)

Calculating what percentage one number is of another number is the second common type of percentage calculation. In this case, division is required followed by converting the decimal to a percentage. If the first number is 100% of the value, the second number will also be 100% if the two numbers are equal; however, this isn't usually the case. If the second number is less than the first number, the second number is less than 100%. If the second number is greater than the first number, the second number is greater than 100%. A simple example is: What percentage of 10 is 6? Because 6 is less than 10, it must also be less than 100% of 10. To calculate, divide 6 by 10 to get 0.6; then convert 0.6 to a percentage by multiplying by 100. 0.6 × 100 = 60%. Therefore, 6 is 60% of 10.

Example question: What percentage of 3700 is 2479? First, recognize that 2479 is less than 3700, so the percentage value must also be less than 100%. Divide 2479 by 3700 and multiply by 100. 2479 ÷ 3700 × 100 = 67%.

• Calculating the Percentage a Whole Number is of Another Whole Number Calculating the Percentage a Whole Number is of Another Whole Number (Percents from 1% to 99%) Calculating the Percentage a Whole Number is of Another Whole Number (Select percents) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 25%)
• Calculating the Percentage a Decimal Number is of a Whole Number Calculating the Percentage a Decimal Number is of a Whole Number (Percents from 1% to 99%) Calculating the Percentage a Decimal Number is of a Whole Number (Select percents) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 25%)
• Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Select percents) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 25%)
• Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Select percents) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 25%)

The third type of percentage calculation involves calculating the original amount from the percentage value and the percentage. The process involved here is the reverse of calculating the percentage value of a number. To get 10% of 100, for example, multiply 100 × 0.10 = 10. To reverse this process, divide 10 by 0.10 to get 100. 10 ÷ 0.10 = 100.

Example question: 4066 is 95% of what original amount? To calculate 4066 in the first place, a number was multiplied by 0.95 to get 4066. To reverse this process, divide to get the original number. In this case, 4066 ÷ 0.95 = 4280.

• Calculating the Original Amount from a Whole Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Whole Numbers ) Calculating the Original Amount (Select percents) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Whole Numbers )
• Calculating the Original Amount from a Decimal Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Decimals ) Calculating the Original Amount (Select percents) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Decimals )
• Calculating the Original Amount from a Whole Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
• Calculating the Original Amount from a Decimal Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )
• Mixed Percentage Calculations with Whole Number Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Whole Numbers )
• Mixed Percentage Calculations with Decimal Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Decimals ) Mixed Percentage Calculations (Select percents) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Decimals )
• Mixed Percentage Calculations with Whole Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
• Mixed Percentage Calculations with Decimal Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )

Percentage Increase/Decrease Worksheets

The worksheets in this section have students determine by what percentage something increases or decreases. Each question includes an original amount and a new amount. Students determine the change from the original to the new amount using a formula: ((new - original)/original) × 100 or another method. It should be straight-forward to determine if there is an increase or a decrease. In the case of a decrease, the percentage change (using the formula) will be negative.

• Percentage Increase/Decrease With Whole Number Percentage Values Percentage Increase/Decrease Whole Numbers with 1% Intervals Percentage Increase/Decrease Whole Numbers with 5% Intervals Percentage Increase/Decrease Whole Numbers with 25% Intervals
• Percentage Increase/Decrease With Decimal Number Percentage Values Percentage Increase/Decrease Decimals with 1% Intervals Percentage Increase/Decrease Decimals with 5% Intervals Percentage Increase/Decrease Decimals with 25% Intervals
• Percentage Increase/Decrease With Whole Dollar Percentage Values Percentage Increase/Decrease Whole Dollar Amounts with 1% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 5% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 25% Intervals
• Percentage Increase/Decrease With Decimal Dollar Percentage Values Percentage Increase/Decrease Decimal Dollar Amounts with 1% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 5% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 25% Intervals

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Percentage word problems

Before you take a look at the percentage word problems in this lesson and their solutions, it may help to review the lesson about  formula for percentage or you can use the different techniques that I use here.

Different types of percentage word problems

There are three different types of percentage word problems. We will show how to solve them using proportions. 

• What is 80% of 20? ( example #1 )
• 50 is 25% of what number? ( example #2 )
• 18 is what percent of 24? What percent of 2000 is 3500? ( example #3 and example #4 )

Solving percentage word problems using proportions

You can solve problems involving percents using the proportion you see in the figure above:   ( n% / 100% = Part / Whole )

First, study the figure carefully! Then, we will show how to use the proportion to solve percentage word problems by creating diagrams to visualize relationships.

Example #1: A test has 20 questions. If peter gets 80% correct, how many questions did peter miss?

First, you need to find the number of correct answers by looking for 80% of 20.

When the problem involves looking for the part or the problem says something like, "Find 80% of 20" or "Find 30% of 50," just change the percent to a decimal and multiply.

80% of 20 = (80 / 100) × 20 = 0.80 × 20 = 16

Since the test has 20 questions and he got 16 correct answers, the number of questions Peter missed is 20 − 16 = 4

Recall that 16 is called the percentage. It is the answer you get when you take the percent of a number.

Percentage  =   Part

Example #2: In a school, 25% of the teachers teach basic math. If there are 50 basic math teachers, how many teachers are there in the school?

Once again set the problem up as shown in the figure below. Notice that the question is, " How many teachers are in the school?"

Therefore, the whole is missing this time!

Method #2 I shall help you reason the problem out!

When we say that 25% of the teachers teach basic math, we mean 25% of all teachers in the school equals number of teachers teaching basic math.

Since we don't know how many teachers there are in the school, we replace this with x or a blank. However, we know that the number of teachers teaching basic math is equal to the percentage = part =  50 Putting it all together, we get the following equation: 25% of ____ = 50 or 25% × ____ = 50 or 0.25 × ____ = 50 Thus, the question is 0.25 times what gives me 50? A simple division of 50 by 0.25 will get you the answer 50 / 0.25 = 200 Therefore, we have 200 teachers in the school In fact, 0.25 × 200 = 50

More percentage word problems

Example #3: 24 students in a class took an algebra test. If 18 students passed the test, what percent do not pass?

Solution First, find out how many student did not pass. Number of students who did not pass is 24 − 18 = 6

Then, write down the following equation: x% of 24 = 6 or x% × 24 = 6

To get x%, just divide 6 by 24 6 / 24 = 0.25 = 25 / 100 = 25% Therefore, 25% of students did not pass.

Example #4: A fundraising company would like to raise $2000 for a cause. The fundraiser was so successful that they ended up raising $3500. What percent of their goal did they raise?

Notice that the whole is 2000 since this is the whole money they expect to raise. The part is the amount that the fundraiser ended with and it usually lower than the amount they expect to raise. However, in this particular case, the part ended up being bigger than the whole. Keeping this in mind, here is how to set it up and solve it!

The fundraising company was able to raise 175% of the expected amount.

Example #5:

A department has a total of 22,000 units of stock. 25% of the garments are black and 10% of the garments are size 14.

a) How many black garments are there? 
b) How many size 14 garments are there? 
c) If 10% of the black garments are size 14,how many garments are black and size 14?

Note that the solution we show below for example #5 use a completely different approach or technique. Read it carefully and try to learn it as well!

25% = 25 per 100 = 250 per 1000 For 22,000 just multiply 250 by 22 250    ×    22   =  250 × (10 + 10 + 2)

                       =  2500 + 2500 + 500                        =  5000 + 500                        =  5500

So, there are 5500 black garments.

10% = 10 per 100 = 100 per 1000 For 22,000 just multiply 100 by 22 100 × 22 = 2200 So, 2200 of the garments are size 14.

If 10% or 10 per 100 of the black garments are size 14, then 100 per 1000 of the black garments are size 14.

500 per 5000 are size 14. However, you need to find it for 5500 black garments.

Then, what is 10% of 500? 10% = 10 per 100, so 50 per 500. So 550 of the black garments are size 14.

If you really understand the percentage word problems above, you can solve any other similar percentage word problems. If you still do not understand them, I strongly encourage you to study them again and again until you get it. The end result will be very rewarding!

Finding a percentage

percentage worksheets

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Word Problems on Percentage

Word problems on percentage will help us to solve various types of problems related to percentage. Follow the procedure to solve similar type of percent problems.

Word problems on percentage:

1.  In an exam Ashley secured 332 marks. If she secured 83 % makes, find the maximum marks.

Let the maximum marks be m.

Ashley’s marks = 83% of m

Ashley secured 332 marks

Therefore, 83% of m = 332

⇒ 83/100 × m = 332

⇒ m = (332 × 100)/83

⇒ m =33200/83

Therefore, Ashley got 332 marks out of 400 marks.

2. An alloy contains 26 % of copper. What quantity of alloy is required to get 260 g of copper?

Let the quantity of alloy required = m g

Then 26 % of m =260 g

⇒ 26/100 × m = 260 g

⇒ m = (260 × 100)/26 g

⇒ m = 26000/26 g

⇒ m = 1000 g

3. There are 50 students in a class. If 14% are absent on a particular day, find the number of students present in the class.

Solution:             

Number of students absent on a particular day = 14 % of 50

                                          i.e., 14/100 × 50 = 7

Therefore, the number of students present = 50 - 7 = 43 students.

4. In a basket of apples, 12% of them are rotten and 66 are in good condition. Find the total number of apples in the basket.

Solution:             

Let the total number of apples in the basket be m

12 % of the apples are rotten, and apples in good condition are 66

Therefore, according to the question,

88% of m = 66

⟹ 88/100 × m = 66

⟹ m = (66 × 100)/88

⟹ m = 3 × 25

Therefore, total number of apples in the basket is 75.

5. In an examination, 300 students appeared. Out of these students; 28 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.

The number of students with first division = 28 % of 300

                                                             = 28/100 × 300

                                                             = 8400/100

                                                             = 84

And, the number of students with second division = 54 % of 300

                                                                        = 54/100 × 300

                                                                        =16200/100

                                                                        = 162

Therefore, the number of students who just passed = 300 – (84 + 162)

                                                                           = 54

Questions and Answers on Word Problems on Percentage:

1. In a class 60% of the students are girls. If the total number of students is 30, what is the number of boys?

2. Emma scores 72 marks out of 80 in her English exam. Convert her marks into percent.

Answer: 90%

3. Mason was able to sell 35% of his vegetables before noon. If Mason had 200 kg of vegetables in the morning, how many grams of vegetables was he able to see by noon?

Answer: 70 kg

4. Alexander was able to cover 25% of 150 km journey in the morning. What percent of journey is still left to be covered?

Answer:  112.5 km

5. A cow gives 24 l milk each day. If the milkman sells 75% of the milk, how many liters of milk is left with him?

Answer: 6 l

6.  While shopping Grace spent 90% of the money she had. If she had $ 4500 on shopping, what was the amount of money she spent?

Answer:  $ 4050

Fraction into Percentage

Percentage into Fraction

Percentage into Ratio

Ratio into Percentage

Percentage into Decimal

Decimal into Percentage

Percentage of the given Quantity

How much Percentage One Quantity is of Another?

Percentage of a Number

Increase Percentage

Decrease Percentage

Basic Problems on Percentage

Solved Examples on Percentage

Problems on Percentage

Real Life Problems on Percentage

Application of Percentage

8th Grade Math Practice From Word Problems on Percentage to HOME PAGE

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25 Percentage Word Problems For Year 5 To Year 8 With Tips On Supporting Pupils’ Progress

Emma Johnson

Percentage word problems and the concept of calculating percentages first appears in Upper Key Stage 2. As pupils progress through school from KS2 to KS3, the skills they need to solve percentage word problems develop.

It is important to expose students to percentage word problems alongside any fluency work on percentages, to help them understand how percentages are used in real-life. To help you with this, we have put together a collection of 25 percentage word problems which can be used by pupils from Year 5 to Year 8. Don’t miss our downloadable word problems worksheet to develop these skills further!

How pupils develop the necessary skills to solve percentage word problems

Percentage word problems in the national curriculum.

• Why are word problems important for children’s understanding of percentage 

How to teach solving percentage word problems in KS2 and early KS3

Percentage word problems for year 5, percentage word problems for year 6, percentage word problems for key stage 3, more word problems resources, percentage word problems faqs.

All Kinds of Word Problems Four Operations

Download this free, printable pack of word problems covering all four operations; a great way to build students' problem solving skills.

Initially, pupils are introduced to the per cent symbol (%) in Year 5. At this stage they are expected to understand that percent relates to ‘number of parts per hundred’ and should be able to solve problems requiring knowing percentage and decimal form equivalents of simple fractions.

As pupils progress into Year 6, they should be able to recall and use equivalences between simple fractions, mixed numbers, decimals and percentages. They also need to be able to solve word problems involving percentages of amounts and percentage increase and decrease.

Moving into Key Stage 3, pupils continue to build on the percentage work from primary, to solve percent problems, interpreting percentages and percentage change; expressing one quantity as a percentage of another; comparing two quantities using percentages and working with percentages greater than 100%.

Concrete resources (such as percentages cubes) and visual images (such as bar models) are important during the early stages of learning and understanding percentages. Word problems for year 3 and word problems for year 4 will often include visual aids. Upper Key Stage 2 teachers and pupils often have the mistaken belief that concrete resources are only for children who are struggling; however, with a new topic, such as percentages, it is important all children are initially introduced to the topic through the use of visual and concrete aids.

Children are first introduced to percentage problems in Year 5. The National Curriculum expectations for percentages are that children will be able to:

Percentage in Year 5

• Recognise the percent symbol (5)  and understand that per cent relates to ‘number of parts per hundred’.
• Write percentages as a fraction with a denominator 100, and in its decimal form.
• Solve problems which require knowing percentage and decimal equivalents of \frac{1}{2},\frac{1}{4},\frac{1}{5},\frac{2}{5},\frac{4}{5} , and fractions with a denominator of a multiple of 10 or 25.

Percentage in Year 6

• Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.
• Solve problems involving the calculation of percentages (for example, measures and such as 15% of 360) and use percentages for comparison.

Percentage in Key Stage 3

• Define percentage as ‘number of parts per hundred’
• Interpret percentages and percentage changes as a fraction or a decimal. Interpret these multiplicatively.
• Express one quantity as a percentage of another.
• Compare two quantities using percentages.
• Work with percentages greater than 100%.
• Interpret fractions and percentages as operators.

Percentage word problems will often include other skills, such as fraction word problems , multiplication word problems , addition word problems , subtraction word problems and division word problems .

Why are word problems important for children’s understanding of percentage 

Percentage word problems help children to develop their understanding of percentages and the different ways percentages are used in everyday life. Taken out of context, percentages can be quite an abstract concept, which some children can find quite difficult to understand. 

Real-life problems involving percentages enable students to see how they will make use of this key skill outside the classroom.

As with all word problems, students need to learn the skills required to solve percentage word problems. It’s important that children make sure they have read the questions carefully and thought about exactly what is being asked and whether they have fully understood this. They then need to identify what they will need to do to solve the problem and whether there are any concrete resources or pictorial representations which they can use to help them. Even pupils in Key Stage 3 can benefit from drawing a quick picture, to understand what a word problem is asking.

Third Space Learning’s online, one-to-one tutoring programmes work to build students’ maths fluency and reasoning skills. Personalised to the needs of each individual student, our programmes fill gaps and build students’ confidence in maths.

Percent word problem example :

A box of cupcakes sold by a bakery cost £3.40.

Due to the increased costs involved with running a bakery, the owner has decided to increase the price of everything sold by 20%.

How much will a box of cupcakes cost once the price has been increased?

How to solve step-by-step:

What do you already know?

–        We know that the original price of a box of cupcakes is £3.40.

–        If the price of the box is being increased by 20%, we need to work out how much 20% of £3.40 is.

–        To do this, we need to work out how much 10% of £3.40 is. We therefore need to divide £3.40 by 10 = £0.34

–        To calculate what 20% is, we need to multiply the £0.34 by 2 = £0.68

–        Finally, we need to add the 20% (£0.68) onto the original price.

–        £3.40 + £0.68 = £4.08

How can this be represented pictorially?

• We can draw a bar model to represent what 10% of £3.40 equals.
• Once we know what 10% of £3.40 is (34p), we can double it to calculate 20% of £3.40 (68p).
• We can then add this on to the original price of £3.40.
• £3.40 + 68p = £4.08.

To solve word problems for year 5 , children need to be able to convert fractions to percentages and calculate fractions of an amount.

Gemma saves \frac{1}{2} of her pocket money every week.

She receives £5 per week and is saving to buy a game costing £25.

• What percentage does she save each week?
• How long will it take her to save for the game?
• She saves 50% of her pocket money each week

Gemma saves £2.50 per week.

£2.50 x 10 = £25

Sam gives \frac{4}{10} of his sweets to Ahmed.

What percentage of the sweets does he keep for himself?

Answer : 60%

  \frac{4}{10} =  \frac{40}{100} = 40%

100 – 40 = 60%

A school football team has 11 players and 5 substitutes.

  \frac{3}{4} of the players are boys, the rest are girls.

What percentage are girls?

Answer: 25%

\frac{3}{4} of 16 are boys

  \frac{1}{4} are girls

  \frac{1}{4} = 25%

Children in Year 5 voted on their favourite food.

35% of children voted for pizza.

60 children took part in the survey.

How many voted for pizza?

Answer : 21 children 

10% of 60: 60 ÷ 10 = 6

5% of 60: Half of 10% (6) = 3

30%: 6 x 3 = 18

35% = 18 + 3 = 21

Ben was given a maths worksheet to complete for his homework.

He got  \frac{6}{10} of the maths problems correct

If there were 20 questions on the paper:

• How many questions did he get right?
• What percentage did he score?

  \frac{1}{10} of 20  = 2

  \frac{6}{10} of 20  = 12

• 60% correct

  \frac{12}{20} =  \frac{60}{100} .

An ice cream seller has been researching the most popular ice creams.

He knows the percentage of each flavour of ice cream sold, but wants to work out how many of each flavour were sold.

80 ice creams were sold in total.

40% vanilla

25% strawberry

20% cookie dough

15% mint choc chip

How many of each ice cream flavour were sold?

20 strawberry

16 cookie dough

12 mint choc chip

10% of 80 = 8 ice creams

5% of 80 = 4 ice creams

Vanilla: 4 x 8 = 32

Strawberry: 2 x 8 = 16. 16 + 4 = 20

Cookie dough: 2 x 8 = 16

Mint choc chip: 8 + 4 = 12

Pupils in Year 5 held a vote on where to go for their next school trip.

The vote was between the zoo and the aquarium.

90 children voted. 

40% voted for the zoo

How many pupils voted for the aquarium?

Answer : 54 children

60% voted for the aquarium

10% of 90 = 9 children

60% = 6 x 9 = 54 children

The price of burgers being sold by a burger van have increased by 25%

If the original price was £2 per burger. How much are the burgers now?

Answer : £2.50

25% of £2 = £2 ÷ 4 = 50p

£2 + 50p = £2.50

Word problems for year 6 involve solving problems involving equivalence between fractions, decimals and percentages; calculation of percentages and using percentages for comparison. Year 6 students will also tackle multi-step problems .

A rugby game lasts for 80 minutes.

A player is on the pitch for 85% of the game.

How long is he on the pitch for?

Answer : 68 minutes

10% of 80  = 8 minutes

5%  = Half of 8 minutes = 4 minutes

80% = 8 x 8 = 64 minutes

64 + 4 = 68 minutes

There are 480 pupils in a primary school.

15% in foundation

25% in Key Stage 1

How many pupils are in Key Stage 2?

Answer : 288 pupils

In foundation there are 15% + 25% (40% of the pupils)

Therefore, 60% of pupils are in KS2

10% of 480 = 48 pupils

60% = 6 x 48 = 288 pupils

A pizza restaurant decided to add a 15% increase to the cost of all their pizzas.

The cost of a meat feast pizza before the increase was £12.60

What is the new price of the pizza?

Answer : £14.49

10% of £12.60 = £1.26

5% = Half of £1.26 = £0.63

15% = £1.26 + £0.63 = £1.89

New price: £12.60 + £1.89 = £14.49

Oliver was shopping for a new pair of jeans.

The jeans were 15% off  in the sale, but the new sale price sticker had fallen off.

The original price of the jeans was £35.

How much did they cost in the sale?

Answer : £29.75

10% of £35 = £3.50

5% = Half of £3.50 = £1.75

35% = £3.50 + £1.75 = £5.25

New price: £35 – £5.25 = £29.75

200g of sugar is needed for a chocolate brownies recipe.

A 1kg bag of sugar is used.

25% of the remaining sugar is used to bake a cake too.

How much sugar was used to bake the cake?

Answer : 200g sugar

 200g sugar used for brownies, therefore 1000g – 200g = 800g remaining

25% of 800g = 800 ÷ 4 = 200g

Mr Jones bought a second hand car for £12,400

A year later, it had decreased in value by 15%

What was the value of the car after a year?

Answer : £10,540

10% of 12,400 = £1,240

5%  = half of £1240 = £620

15% = 1240 + 620 = £1,860

Value after a year = 12,400 – 1860 = £10,540

The number of visitors to a theme park in 2021 was 286,000.

The following year, there was a 24 percent increase in visitors.

How many visited the theme park in 2022?

Answer : 354,640 visitors

10% of 286,000 = 28,600

20% = 2 x 28,600 = 57,200

1% of 286,000 = 2,860

4% = 4 x 2860 = 11,440

24% = 57,200 + 11,440 = 68.640

Total number of visitors: 286,000 + 68,640 = 354,640

A library has 16,200 books

55% are fiction and 45% are non-fiction

968 non-fiction books are taken out in one week.

How many non-fiction books are left in the library, from the books which were there at the start of the week? 

Answer : 6,322 non-fiction books

10% of 16,200 = 1,620

40% = 1,620 x 4 = 6,480 books

5% = half of 1,620 = 810

45% = 6,480 + 810 = 7,290

7,290 – 968 = 6,322

In Key Stage 3, the work pupils carry out on percentages, builds upon the percentage skills developed in primary. Students need to be able to solve percent word problems involving interpreting percentages and percentage change as a fraction or decimal; expressing one quantity as a percentage of another; comparing two quantities using percentages; working with percentages greater than 100% and interpreting fractions and percentages as operators.

Jasmine wins £600

She gives 30% to her sister and 20% to her friend.

She keeps the rest.

How much does each person have?

Sister: £180

Friend: £120

Jasmine: £300

She gives 30% to her sister.

10% of £600 = £60

30% = 3 x 60 = £180

She gives 20% to her friend.

20% = 2 x 60 = £120

She must keep 50% for herself, if she has given 30% and 40% away.

50% of 600 =  \frac{1}{2} of 600 = £300

A car is reduced in the sale by 15%

If the original price was £18,500, what is the price of the car now?

Answer: £16,225

10% of 18500 = 1,850

5% = half of 1,850 = £925

15% = 1,850 + 925 = £2,275

New price: 18,500 – 2,275 = £16,225

Sales tax in Florida is 6%

Maisie has bought a pair of jeans, 3 T shirts and a jacket, which came to $150

How much will she have to pay, once she has added on the sales tax?

Answer: $159

1% of 150 = 1.5

6% = 6 x 1.5 = $9

150 + 9 = $159

A packet of biscuits is 300g

As a special offer, the biscuits currently have an extra 15% free.

How many grams of biscuit do you get with the special offer?

Answer : 345g

10% of 300 = 30g

5% = half of 30 = 15g

15% = 30 + 15 = 45g

New weight: 300 + 45 = 345g

Jason is travelling to Birmingham from Manchester.

His average speed is 62 miles per hour

On the return journey, the traffic on the M6 is terrible and his average speed it reduced by 35%

What is his average speed on the return journey?

Answer : 40.3mph

10% of 62 = 6.2mph

30% = 6.2 x 3 = 18.6mph

5% = half of 6.2 = 3.1mph

35% = 18.6 + 3.1 = 21.7mph

62 – 21.7 = 40.3 mph

Mr Andrews bought a car in January 2021 for £15000.

By January 2022 his car had depreciated in value by 20%.

By January 2023, his car had depreciated in value by another 30%.

What was the value of his car in January 2023?

Answer : £8400

January 2022

20% of £15000 = £3000, so the value of the car is £12000.

January 2023

30% of £12000 = £3600, so the value of the car is £8400.

Alternative method – using decimal multiplier

20% decrease means 80% of January 2021 value – decimal multiplier of 0.8

30% decrease means 70% of January 2022 value – decimal multiplier of 0.7

15000 x 0.8 x 0.7 = £8400.

In her half term test, Jasmine did a French test and scored 15 out of 30.

In her next half term test, Jasmine scored 21 out of 30 in her French test.

By what percentage did Jasmine improve?

Answer : 40% improvement

Percentage change

= 21 – 15/15  x 100

= 6/15  x 100 = 40% improvement.

In 2021, a company made a profit of $600000.

In 2022, the same company made a profit of $1350000.

By what percentage had their profit increased?

Answer : 125% improvement

= 1350000 – 600000/600000 x 100

= 750000/600000 x 100 = 125% improvement.

In 2022, Thomas earned £1800 a month for his job.

As part of his annual review in February 2023, he is going to ask for a pay rise of 3.5%.

If the pay rise is agreed, what will Thomas’ annual salary be?

Answer: £22356

3.5% of £1800 = £63

So new monthly salary would be £1863

£1863 x 12 = £22356.

Alternative method 1

£1800 x 12 = £21600

3.5% of £21600 = £756

£21600 + £756 = £22356.

Looking for more word problems practice questions? Take a look at our collection of addition and subtraction word problems , time word problems , money word problems and ratio word problems . Teaching percentages to KS3 or KS4? Check out our percentage worksheets here.

There are different types of percentage problems. If you want to find the percentage of an amount, it can be calculated by writing the percentage as a decimal or a fraction and then multiplying it by the amount.

Pupils in Year 5 held a vote on where to go for their next school trip. The vote was between the zoo and the aquarium. 90 children voted.  40% voted for the zoo How many pupils voted for the aquarium?

1. Calculating a discount when shopping 2. Understanding bank interest rates 3. Understanding your grades in school

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Course: 6th grade   >   Unit 3

• Finding a percent

Finding percents

• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
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Harvey Weinstein Conviction Thrown Out

New york’s highest appeals court has overturned the movie producer’s 2020 conviction for sex crimes, which was a landmark in the #metoo movement..

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When the Hollywood producer Harvey Weinstein was convicted of sex crimes four years ago, it was celebrated as a watershed moment for the #MeToo movement. Yesterday, New York’s highest court of appeals overturned that conviction.

Jodi Kantor, one of the reporters who broke the story of the abuse allegations against Mr. Weinstein in 2017, explains what this ruling means for him and for #MeToo.

On today’s episode

Jodi Kantor , an investigative reporter for The New York Times.

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