percentage problem solving pdf

Percentage Word Problem Worksheets

Percentages can be calculated from fractions and decimals. Although there are many steps to calculate a percentage, it can be simplified a bit. Multiplication is used if you work with a decimal, and division is used to convert a mixed number to a percentage.

The word percentage means 100 percent. For example, 10 percent means 10 out of 100. This can be written as 10 or 10% or as a fraction of 10/100, or as a decimal such as .10. It can look at numbers written in different formats and choose them as potential percentages can help students prepare for tests.

Benefits of Percentage Word Problem Worksheets

Cuemath's interactive math worksheets consist of visual simulations to help your child visualize the concepts being taught, i.e., "see things in action and reinforce learning from it." The percentage word problem worksheets follow a step-by-step learning process that helps students better understand concepts, recognize mistakes, and possibly develop a strategy to tackle future problems and In the Percent Problems Worksheet, we will also practice different types of questions about calculating percentage word problems.

Download Percentage Word Problem Worksheet PDFs

Percentages Practice Questions

Percentages (non-calculator), click here for questions, click here for answers, percentages (calculator), gcse revision cards.

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18.4: Solving Percentage Problems

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Let's solve more percentage problems.

Exercise \(\PageIndex{1}\): Number Talk: Multiplication with Decimals

Find the products mentally.

\(6\cdot (0.8)\cdot 2\)

\((4.5)\cdot (0.6)\cdot 4\)

Exercise \(\PageIndex{2}\): Coupons

Han and Clare go shopping, and they each have a coupon. Answer each question and show your reasoning.

• Han buys an item with a normal price of $15, and uses a 10% off coupon. How much does he save by using the coupon?

• Clare buys an item with a normal price of $24, but saves $6 by using a coupon. For what percentage off is this coupon?

Are you ready for more?

Clare paid full price for an item. Han bought the same item for 80% of the full price. Clare said, “I can’t believe I paid 125% of what you paid, Han!” Is what she said true? Explain.

Exercise \(\PageIndex{3}\): Info Gap: Music Devices

Your teacher will give you either a problem card or a data card . Do not show or read your card to your partner.

If your teacher gives you the problem card :

• Silently read your card and think about what information you need to be able to answer the question.
• Ask your partner for the specific information that you need.
• Explain how you are using the information to solve the problem. Continue to ask questions until you have enough information to solve the problem.
• Share the problem card and solve the problem independently.
• Read the data card and discuss your reasoning.

If your teacher gives you the data card :

• Silently read your card.
• Ask your partner “What specific information do you need?” and wait for them to ask for information. If your partner asks for information that is not on the card, do not do the calculations for them. Tell them you don’t have that information.
• Before sharing the information, ask “ Why do you need that information? ” Listen to your partner’s reasoning and ask clarifying questions.
• Read the problem card and solve the problem independently.
• Share the data card and discuss your reasoning.

A pot can hold 36 liters of water. What percentage of the pot is filled when it contains 9 liters of water?

Here are two different ways to solve this problem:

• Using a double number line:

We can divide the distance between 0 and 36 into four equal intervals, so 9 is \(\frac{1}{4}\) of 36, or 9 is 25% of 36.

• Using a table:

Glossary Entries

Definition: Percent

The word percent means “for each 100.” The symbol for percent is %.

For example, a quarter is worth 25 cents, and a dollar is worth 100 cents. We can say that a quarter is worth 25% of a dollar.

Definition: Percentage

A percentage is a rate per 100.

For example, a fish tank can hold 36 liters. Right now there is 27 liters of water in the tank. The percentage of the tank that is full is 75%.

Exercise \(\PageIndex{4}\)

For each problem, explain or show your reasoning.

• 160 is what percentage of 40?
• 40 is 160% of what number?
• What number is 40% of 160?

Exercise \(\PageIndex{5}\)

A store is having a 20%-off sale on all merchandise. If Mai buys one item and saves $13, what was the original price of her purchase? Explain or show your reasoning.

Exercise \(\PageIndex{6}\)

The original price of a scarf was $16. During a store-closing sale, a shopper saved $12 on the scarf. What percentage discount did she receive? Explain or show your reasoning.

Exercise \(\PageIndex{7}\)

Select all the expressions whose value is larger than 100.

• 120% of 100
• 500% of 400
• 1% of 1,000

Exercise \(\PageIndex{8}\)

An ant travels at a constant rate of 30 cm every 2 minutes.

• At what pace does the ant travel per centimeter?
• At what speed does the ant travel per minute?

(From Unit 3.3.4)

Exercise \(\PageIndex{9}\)

Is \(3\frac{1}{2}\) cups more or less than 1 liter? Explain or show your reasoning. (Note: 1 cup \(\approx\) 236.6 milliliters)

(From Unit 3.2.3)

Exercise \(\PageIndex{10}\)

Name a unit of measurement that is about the same size as each object.

• The distance of a doorknob from the floor is about 1 _____________.
• The thickness of a fingernail is about 1 _____________.
• The volume of a drop of honey is about 1 _____________.
• The weight or mass of a pineapple is about 1 _____________.
• The thickness of a picture book is about 1 _____________.
• The weight or mass of a buffalo is about 1 _____________.
• The volume of a flower vase is about 1 _____________.
• The weight or mass of 20 staples is about 1 _____________.
• The volume of a melon is about 1 _____________.
• The length of a piece of printer paper is about 1 _____________.

(From Unit 3.2.1)

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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Solved Examples on Percentage

The solved examples on percentage will help us to understand how to solve step-by-step different types of percentage problems. Now we will apply the concept of percentage to solve various real-life examples on percentage.

Solved examples on percentage:

1.  In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate.

Total number of invalid votes = 15 % of 560000

                                       = 15/100 × 560000

                                       = 8400000/100

                                       = 84000

Total number of valid votes 560000 – 84000 = 476000

Percentage of votes polled in favour of candidate A = 75 %

Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000

= 75/100 × 476000

= 35700000/100

2. A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 8% of bananas were rotten. Find the percentage of fruits in good condition.

Total number of fruits shopkeeper bought = 600 + 400 = 1000

Number of rotten oranges = 15% of 600

                                    = 15/100 × 600

                                    = 9000/100

                                    = 90

Number of rotten bananas = 8% of 400

                                   = 8/100 × 400

                                   = 3200/100

                                   = 32

Therefore, total number of rotten fruits = 90 + 32 = 122

Therefore Number of fruits in good condition = 1000 - 122 = 878

Therefore Percentage of fruits in good condition = (878/1000 × 100)%

                                                                 = (87800/1000)%

                                                                 = 87.8%

3. Aaron had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he take along with him?

Solution:            

Let the money he took for shopping be m.

Money he spent = 30 % of m

                      = 30/100 × m

                      = 3/10 m

Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10

But money left with him = $ 2100

Therefore 7m/10 = $ 2100          

m = $ 2100× 10/7

m = $ 21000/7

Therefore, the money he took for shopping is $ 3000.

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

Problems on Percentage

Real Life Problems on Percentage

Word Problems on Percentage

Application of Percentage

8th Grade Math Practice From Solved Examples on Percentage to HOME PAGE

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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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