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

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

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

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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Solving problems with percentages

  • Price difference I
  • Price difference II
  • How many students?

To solve problems with percent we use the percent proportion shown in "Proportions and percent".

$$\frac{a}{b}=\frac{x}{100}$$

$$\frac{a}{{\color{red} {b}}}\cdot {\color{red} {b}}=\frac{x}{100}\cdot b$$

$$a=\frac{x}{100}\cdot b$$

x/100 is called the rate.

$$a=r\cdot b\Rightarrow Percent=Rate\cdot Base$$

Where the base is the original value and the percentage is the new value.

47% of the students in a class of 34 students has glasses or contacts. How many students in the class have either glasses or contacts?

$$a=r\cdot b$$

$$47\%=0.47a$$

$$=0.47\cdot 34$$

$$a=15.98\approx 16$$

16 of the students wear either glasses or contacts.

We often get reports about how much something has increased or decreased as a percent of change. The percent of change tells us how much something has changed in comparison to the original number. There are two different methods that we can use to find the percent of change.

The Mathplanet school has increased its student body from 150 students to 240 from last year. How big is the increase in percent?

We begin by subtracting the smaller number (the old value) from the greater number (the new value) to find the amount of change.

$$240-150=90$$

Then we find out how many percent this change corresponds to when compared to the original number of students

$$90=r\cdot 150$$

$$\frac{90}{150}=r$$

$$0.6=r= 60\%$$

We begin by finding the ratio between the old value (the original value) and the new value

$$percent\:of\:change=\frac{new\:value}{old\:value}=\frac{240}{150}=1.6$$

As you might remember 100% = 1. Since we have a percent of change that is bigger than 1 we know that we have an increase. To find out how big of an increase we've got we subtract 1 from 1.6.

$$1.6-1=0.6$$

$$0.6=60\%$$

As you can see both methods gave us the same answer which is that the student body has increased by 60%

Video lessons

A skirt cost $35 regulary in a shop. At a sale the price of the skirtreduces with 30%. How much will the skirt cost after the discount?

Solve "54 is 25% of what number?"

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Percent Maths Problems

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Percentage Word Problems 5th Grade

Welcome to our Percentage Word Problems. In this area, we have a selection of percentage problem worksheets for 5th grade designed to help children learn to solve a range of 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

Percentage Word Problems

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.

Percentage of Calculator image

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.

Convert fractions to percentages Picture

  • Converting Fractions to Percentages

Convert Percent to Fraction Image

  • 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!

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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

Mixed Percent Problems with Whole Number Amounts and Multiples of 5 Percents

Percentage Calculations

problem solving and percentages

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

problem solving and percentages

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 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.

problem solving and percentages

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)

= Rs. [(120/100) x (75/100) x 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

= Rs. [8748 x (10/9) x (10/9 ) x (10/9)]

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

⇒ x = 360

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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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

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Application of Percentage

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Mr. Mathematics

Solving Problems with Percentages

March 12, 2023.

Scheme of work: GCSE Higher: Year 10: Term 1: Solving Problems with Percentages

Prerequisite Knowledge

  • Multiply and divide by powers of ten.
  • Recognise the per cent symbol (%)
  • Understand that per cent relates to number of parts per hundred.
  • Write one number as a fraction of another
  • Calculate equivalent fractions

Success Criteria

  • Define percentage as a number of parts per hundred.
  • Interpret fractions and percentages as operators
  • Interpret percentages as a fraction or a decimal
  • Interpret percentages changes as a fraction or a decimal
  • Interpret percentage changes multiplicatively
  • Express one quantity as a percentage of another
  • Compare two quantities using percentages
  • Work with percentages greater than 100%;
  • Solve problems involving percentage change
  • Solve problems involving percentage increase/decrease
  • Solve problems involving original value problems
  • Solve problems involving simple interest including in financial mathematics
  • Set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes

Key Concepts

  • Use the place value table to illustrate the equivalence between fractions, decimals and percentages.
  • To calculate a percentage of an amount without calculator students need to be able to calculate 10% of any number by dividing by 10.
  • To calculate a percentage of an amount with a calculator students should be able to convert percentages to decimals mentally and use the percentage function.
  • Equivalent ratios are useful for calculating the original amount after a percentage change.
  • To calculate the multiplier for a percentage change students need to understand 100% as the original amount. E.g., 10% decrease represents 10% less than 100% = 0.9.
  • Students need to have a secure understanding of the difference between simple and compound interest.

Common Misconceptions

  • Students often consider percentages to be limited to 100%. A key learning point is to understand how percentages can exceed 100%.
  • Students sometimes confuse 70% with a magnitude of 70 rather than 0.7.
  • Students can confuse 65% with 1/65 rather than 65/100.
  • Compound interest is often confused with simple interest, i.e., 10% compound interest = 110% = 1.1 2,  not 220% (2.2).

Solving Problems with Percentages Resources

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Florida legislators look at issue of students who miss too much school

TALLAHASSEE — Florida lawmakers during the coming legislative session could look to address the problem of chronic absenteeism among public-school students.

Data collected by the Florida Department of Education showed that 20.9 percent of students in public schools, including students in adult education courses, missed 21 or more school days during the 2021-2022 academic year.

In measuring student attendance, the department looks at students who miss 21 or more days and students absent for 10 percent or more of the academic year. The 2021-2022 data showed that 32.3 percent of students, or more than 1 million students, were absent for 10 percent or more of the year.

Members of the House Education Quality Subcommittee this month heard from experts on chronic absenteeism as lawmakers prepare for the Jan. 9 start of the 2024 legislative session.

Chronic absenteeism can involve missing school for any reason, including excused and unexcused absences and suspensions.

“If you are chronically absent, it actually predicts higher suspension rates, lower achievement in middle school and a greater likelihood to drop out of high school,” said Hedy Chang, founder and executive director of the group Attendance Works, which works nationally on addressing school absenteeism issues.

High rates of absenteeism also can exacerbate problems such as lagging third-grade literacy skills — which is a key indicator of future academic success, according to the group.

Reasons for absenteeism can include a range of factors, from socioeconomic status to access to health care to older siblings being responsible for getting younger siblings to school.

Inika Williams, associate director of policy for Attendance Works, told the House panel that in Leon County, where she lives, “there are 13,000 children who are unable to make it to school regularly.”

“Even if you look at Leon County schools data, most of your Title I schools and most of your schools where there’s high concentrations of poverty have the highest chronic absenteeism rates,” Williams said.

Paul Burns, a chancellor with the Department of Education, said during the meeting that “the circumstances that a family and student may be facing are really individualized.”

Absenteeism rates have been rising nationwide, Attendance Works said on its website.

“Chronic absence appears to have doubled by the end of the 2021-22 school year. We estimate that it now affects nearly one out of three students (or 16 million vs. 8 million students in the 2018-19 school year),” the website said.

A comparison of data going back more than a decade, housed on the Florida Department of Health website, showed that the 20.9 percent of students missing 21 or more days during the 2021-2022 school year represented the highest rate of absenteeism in the state since at least 2010.

The Department of Health website said chronic absenteeism “is prevalent among all races and among students with disabilities.”

Data from the Department of Education showed that 31.4 percent of students designated chronically absent during the 2021-2022 year were white, 37.9 percent were Hispanic and 24.9 percent were Black.

Solving the problem could involve multi-faceted solutions.

Burns pointed to what are known as academic study teams, which include school administrators, counselors, teachers, social workers and psychologists, “collaboratively focusing” and helping address barriers that families face to improving attendance.

Chang said getting families involved is crucial in helping to improve attendance rates.

“We know that chronic absence is higher when kids have adverse early childhood experiences. When that happens, the key is not saying, ‘What’s wrong with you?’ But, ‘What happened, how can I help you?’ And to engage students and families in a problem-solving way so we can address the challenges that cause them to miss school in the first place,” Chang told the House panel.

House Education Quality Chairwoman Dana Trabulsy, R-Fort Pierce, said during the meeting that members “have not heard the last of chronic absenteeism in this committee.”

“If we are not helping children to realize that school is important, then how are they going to realize that work is important? How are they going to show up to work? These are our future leaders and we need to invest more in this important topic,” Trabulsy said.

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Problem-solving skills training may improve parental psychosocial outcomes

by Elana Gotkine

Problem-solving skills training can improve parental psychosocial outcomes

For parents of children with chronic health conditions (CHCs), problem-solving skills training (PSST) is associated with improvement in parental, pediatric, and family psychosocial outcomes, according to a review published online Jan. 2 in JAMA Pediatrics .

Tianji Zhou, Ph.D., from the Xiangya School of Nursing at Central South University in Changsha, China, and colleagues conducted a systematic review of randomized clinical trials (RCTs) to examine the associations of PSST for parents of children with CHCs with parental, pediatric, and family psychosocial outcomes. Twenty-three RCTs involving 3,141 parents were included in the systematic review ; 21 were eligible for meta-analysis.

The researchers found that PSST was significantly associated with improvements in parental outcomes, including problem-solving skills, depression, distress, posttraumatic stress, parenting stress, and quality of life (QOL; standardized mean differences [SMDs], 0.43, −0.45, −0.61, −0.39, −0.62, and 0.45, respectively).

PSST was associated with better QOL and fewer mental problems for children (SMD, 0.76 and −0.51, respectively) and with less parent-child conflict (SMD, −0.38). PSST was more efficient for parents of children aged 10 years or younger or who were newly diagnosed with a CHC in subgroup analysis. PSST delivered online was associated with significant improvements in most outcomes.

"Our findings on children- and intervention-level characteristics may guide the design and delivery of future PSST by presenting information on factors associated with effectiveness," the authors write.

Copyright © 2024 HealthDay . All rights reserved.

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IMAGES

  1. Solving Percent Problems (examples, solutions, worksheets, videos

    problem solving and percentages

  2. Percentage Word Problems

    problem solving and percentages

  3. Solving Percentage Word Problems

    problem solving and percentages

  4. 6th Grade Math: Percent, Percent and more percent!

    problem solving and percentages

  5. How to Solve Percent Problems? (13 Amazing Examples!)

    problem solving and percentages

  6. Solving Percent Problems Worksheet

    problem solving and percentages

VIDEO

  1. What is 32% of 140?

  2. easy tricks to solve problems on percentages #shorts #shortvideo

  3. Solving Percentage Problems|| Lecture 21||Urdu

  4. Solving percentages শতকরা অংকের সমাধান খুবই সহজ উপায়ে

  5. Finding a percentage

  6. Multiple Step Percent Problem #SAT

COMMENTS

  1. Percentages

    In word problems involving percentages, remember that the sum of all parts of the whole is 100 % ‍ . For example, if a teacher has graded 60 % ‍ of an assignment, then they have not graded 100 − 60 % = 40 % ‍ of the assignment. 60 % ‍ and 40 % ‍ are complementary percentages: they add up to 100 % ‍ .

  2. How to Solve Percent Problems

    Percent problems can seem intimidating. But if you remember the relationship between percents and fractions, you'll be on your way. ... But an easy way of solving the problem is to switch it around: 88% of 50 = 50% of 88. This move is perfectly valid, and it makes the problem a lot easier. As you learned above, 50% of 88 is simply half of 88:

  3. Solving percent problems (video)

    Solving percent problems Equivalent expressions with percent problems Percent word problem: magic club Percent problems Percent word problems: tax and discount Tax and tip word problems Percent word problem: guavas Discount, markup, and commission word problems Multi-step ratio and percent problems Math > 7th grade > Rates and percentages >

  4. 5.2.1: Solving Percent Problems

    To solve percent problems, you can use the equation, Percent ⋅ Base = Amount , and solve for the unknown numbers. Or, you can set up the proportion, Percent = amount base , where the percent is a ratio of a number to 100. You can then use cross multiplication to solve the proportion. Percents are a ratio of a number and 100, so they are ...

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

    Solution: 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\)? Solution: In this problem, we are looking for the percent. Use the following equation:

  6. Percent problems (practice)

    Solving percent problems Equivalent expressions with percent problems Percent word problem: magic club Percent problems Percent word problems: tax and discount Tax and tip word problems Percent word problem: guavas Discount, markup, and commission word problems Multi-step ratio and percent problems Math > 7th grade > Rates and percentages >

  7. Solving problems with percentages (Pre-Algebra, Ratios and percent

    To solve problems with percent we use the percent proportion shown in "Proportions and percent". a b = x 100 a b = x 100 a b ⋅b = x 100 ⋅ b a b ⋅ b = x 100 ⋅ b a = x 100 ⋅ b a = x 100 ⋅ b x/100 is called the rate. a = r ⋅ b ⇒ Percent = Rate ⋅ Base a = r ⋅ b ⇒ P e r c e n t = R a t e ⋅ B a s e

  8. 4.2: Percents Problems and Applications of Percent

    College Technical Math 1A (NWTC) 4: Percents

  9. Percent word problems (practice)

    Course: 6th grade > Unit 3. Lesson 6: Percent word problems. Percent word problem: recycling cans. Percent word problems. Rates and percentages FAQ. Math. 6th grade. Percent word problems.

  10. Solving percent problems

    Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fr...

  11. 7.3: Solving Basic Percent Problems

    Divide: 15/50 = 0.30. 15 = 50 x Original equation. 15 50 = 50 x 50 Divide both sides by 50. 15 50 = x Simplify right-hand side. x = 0.30 Divide: 15/50 = 0.30. But we must express our answer as a percent. To do this, move the decimal two places to the right and append a percent symbol. Thus, 15 is 30% of 50.

  12. 18.4: Solving Percentage Problems

    Here are two different ways to solve this problem: Using a double number line: Figure 18.4.2 18.4. 2. We can divide the distance between 0 and 36 into four equal intervals, so 9 is 1 4 1 4 of 36, or 9 is 25% of 36. Using a table:

  13. Percent Maths Problems

    Solution to Problem 1 The absolute decrease is 20 - 15 = $5 The percent decrease is the absolute decrease divided by the the original price (part/whole). percent decease = 5 / 20 = 0.25 Multiply and divide 0.25 to obtain percent. percent decease = 0.25 = 0.25 * 100 / 100 = 25 / 100 = 25% Problem 2 Mary has a monthly salary of $1200.

  14. Percentages

    . The whole is 24 . 21 24 ⋅ 100 = 87.5 % If we have any two of the part, the whole, and the percentage, we can solve for the missing value! Note: be careful when identifying the part and the whole; the part won't necessarily be the smaller number! Example: What is 150 % of 8 ? [Show me!] Finding complementary percentages

  15. Percentage Calculator

    Find a percentage or work out the percentage given numbers and percent values. Use percent formulas to figure out percentages and unknowns in equations. Add or subtract a percentage from a number or solve the equations. How to Calculate Percentages. There are many formulas for percentage problems. You can think of the most basic as X/Y = P x 100.

  16. Percentage Word Problems

    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.

  17. Percentages Practice Questions

    Click here for Questions Click here for Answers Percentages (calculator) Click here for Questions Click here for Answers Practice Questions Previous Foundation Solving Quadratics Next Ratio Videos The Corbettmaths Practice Questions on finding a percentage of an amount.

  18. Solving Percent Problems

    Percent problems have three parts: the percent, the base (or whole), and the amount. Any of those parts may be the unknown value to be found. To solve percent problems, you can use the equation, Percent · Base = Amount, and solve for the unknown numbers. Or, you can set up the proportion, Percent = , where the percent is a ratio of a number to 100.. You can then use cross multiplication to ...

  19. PDF Percent Equation P B A

    Given: Base = 120 Unknown: Percent = x Amount = 15 Equation: 120 • x = 15 120• x 15 120 120 x 0.125 12.5% = == 0.125 120 15.000 Percent Proportion Problems involving the percent equation can also be solved with the proportion: Percent Amount (is) 100 Base (of) = When the percent is given, drop the percent sign and place the percent over 100.

  20. Percentages Worksheets

    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)

  21. Percentage Questions (with Answers)

    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 = 64 % 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

  22. Solved 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.

  23. Solving Problems with Percentages

    Lesson 1. Converting between fractions decimals and percentages Lesson 2. Writing Percentages Lesson 3. Percentage Increases Lesson 4. Percentage Decreases Lesson 5. Reverse Percentages Lesson 6. Compound Percentage Increases Lesson 7. Compound Percentage Decrease Lesson 8. Calculating a Repeated Percentage Change Extended Learning Online Lesson

  24. 14 Effective Problem-Solving Strategies

    14 types of problem-solving strategies. Here are some examples of problem-solving strategies you can practice using to see which works best for you in different situations: 1. Define the problem. Taking the time to define a potential challenge can help you identify certain elements to create a plan to resolve them.

  25. The Performance Review Problem

    Nearly half (49 percent) of companies give annual or semiannual reviews, according to a study of 1,000 full-time U.S. employees released late last year by software company Workhuman.

  26. Legislature: 21 percent of Florida students are chronically absent

    The 2021-2022 data showed that 32.3 percent of students, or more than 1 million students, were absent for 10 percent or more of the year. ... Solving the problem could involve multi-faceted ...

  27. Problem-solving skills training may improve parental psychosocial outcomes

    The researchers found that PSST was significantly associated with improvements in parental outcomes, including problem-solving skills, depression, distress, posttraumatic stress, parenting stress ...

  28. Poor sleep in your 30s linked to memory and thinking problems in later life

    Science Reporter. 0. Disrupted sleep in your 30s and 40s can lead to cognitive problems in later life, scientists say. As of 2014, an estimated 5 million American adults over 65 were living with ...